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Copy file name to clipboardExpand all lines: code_extra/bib_preset.yml
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HKSbasics:
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W. C. Huffman, J.-L. Kim, and P. Solé, "Basics of coding theory." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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W. C. Huffman, J.-L. Kim, and P. Solé, "Basics of coding theory." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 3-44 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKScyclic:
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_ready_formatted:
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flm: >-
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C. Ding, "Cyclic Codes over Finite Fields." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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C. Ding, "Cyclic Codes over Finite Fields." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 45-60 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSclass:
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flm: >-
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P. R. J. Östergård, "Construction and Classification of Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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P. R. J. Östergård, "Construction and Classification of Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 61-78 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSselfdual:
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flm: >-
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S. Bouyuklieva, "Self-dual codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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S. Bouyuklieva, "Self-dual codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 79-96 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSdesigns:
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flm: >-
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V. D. Tonchev, "Codes and designs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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V. D. Tonchev, "Codes and designs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 97-110 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSrings:
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flm: >-
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S. T. Dougherty, "Codes over rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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S. T. Dougherty, "Codes over rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 111-128 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSconstacyclicrings:
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flm: >-
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H. Q. Dinh, S. R. López-Permouth, "Constacyclic Codes over Finite Commutative Chain Rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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H. Q. Dinh, S. R. López-Permouth, "Constacyclic Codes over Finite Commutative Chain Rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 385-428 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSquasicyclic:
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# _ready_formatted:
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# flm: >-
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# C. Güneri, S. Ling, B. Özkaya, "Quasi-cyclic codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# C. Güneri, S. Ling, B. Özkaya, "Quasi-cyclic codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 129-150 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSskewcyclic:
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# flm: >-
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# H. Gluesing-Luerssen, "Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# H. Gluesing-Luerssen, "Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 151-180 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSadditivecyclic:
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# flm: >-
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# J. Bierbrauer, S. Marcugini, F. Pambianco, "Additive cyclic codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# J. Bierbrauer, S. Marcugini, F. Pambianco, "Additive cyclic codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 181-196 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSconvolutional:
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# flm: >-
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# J. Lieb, R. Pinto, J. Rosenthal, "Convolutional codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# J. Lieb, R. Pinto, J. Rosenthal, "Convolutional codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 197-226 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSrankmetric:
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# _ready_formatted:
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# flm: >-
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# E. Gorla, "Rank-metric codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# E. Gorla, "Rank-metric codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 227-250 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSbounds:
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flm: >-
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P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 251-266 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSpolar:
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flm: >-
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N. Presman, S. Litsyn, "Polar codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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N. Presman, S. Litsyn, "Polar codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 763-784 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSsemidefinite:
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# _ready_formatted:
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# flm: >-
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# F. Vallentin, "Semidefinite Programming Bounds for Error-Correcting Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# F. Vallentin, "Semidefinite Programming Bounds for Error-Correcting Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 267-282 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSprojective:
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flm: >-
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L. Storme, "Coding Theory and Galois Geometries." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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L. Storme, "Coding Theory and Galois Geometries." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 285-310 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSag:
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flm: >-
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A. Couvreur, H. Randriambololona, "Algebraic Geometry Codes and Some Applications." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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A. Couvreur, H. Randriambololona, "Algebraic Geometry Codes and Some Applications." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 311-362 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSalgebra:
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flm: >-
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W. Willems, "Codes in Group Algebras." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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W. Willems, "Codes in Group Algebras." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 363-384 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKStrace:
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# flm: >-
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# M. Shi, "Weight Distribution of Trace Codes over Finite Rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# M. Shi, "Weight Distribution of Trace Codes over Finite Rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 429-448 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKStwoweight:
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flm: >-
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A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 449-462 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSfunctions:
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# flm: >-
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# S. Mesnager, "Linear Codes from Functions." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# S. Mesnager, "Linear Codes from Functions." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 463-526 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSgraphs:
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flm: >-
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C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 527-552 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSmetrics:
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flm: >-
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M. Firer, "Alternative Metrics." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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M. Firer, "Alternative Metrics." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 555-574 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSalgo:
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# M. Wassermann, "Algorithmic Methods." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# M. Wassermann, "Algorithmic Methods." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 575-598 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSlattice:
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# F. Oggier, "Lattice Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# F. Oggier, "Lattice Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 645-656 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSquantum:
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flm: >-
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M. F. Ezerman, "Quantum Error-Control Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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M. F. Ezerman, "Quantum Error-Control Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 657-672 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSstc:
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flm: >-
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F. Oggier, "Space-Time Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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F. Oggier, "Space-Time Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 673-684 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSnetwork:
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flm: >-
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F. R. Kschischang, "Network Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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F. R. Kschischang, "Network Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 685-714 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSdist:
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flm: >-
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V. Ramkumar, M. Vajha, S. B. Balaji, M. N. Krishnan, B. Sasidharan, P. Vijay Kumar, "Codes for Distributed Storage." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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V. Ramkumar, M. Vajha, S. B. Balaji, M. N. Krishnan, B. Sasidharan, P. Vijay Kumar, "Codes for Distributed Storage." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 735-762 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSfountain:
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flm: >-
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I. F. Blake, "Coding for Erasures and Fountain Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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I. F. Blake, "Coding for Erasures and Fountain Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 715-734 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSinterp:
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# S. Kopparty, "Interpolation Decoding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# S. Kopparty, "Interpolation Decoding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 599-612 \href{https://doi.org/10.1201/9781315147901}{DOI}
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HKSpseudo:
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T. Helleseth, C. Li, "Pseudo-Noise Sequences." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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T. Helleseth, C. Li, "Pseudo-Noise Sequences." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 613-644 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKSsecretsharing:
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# C. Ding, "Secret Sharing with Linear Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# C. Ding, "Secret Sharing with Linear Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 785-798 \href{https://doi.org/10.1201/9781315147901}{DOI}
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# HKScrypto:
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# P. Gaborit, J.-C. Deneuville, "Code-Based Cryptography." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) \href{https://doi.org/10.1201/9781315147901}{DOI}
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# P. Gaborit, J.-C. Deneuville, "Code-Based Cryptography." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 799-822 \href{https://doi.org/10.1201/9781315147901}{DOI}
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KLbounds:
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@@ -624,12 +624,12 @@ Sidelnikov97:
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Sloane04:
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N. J. A. Sloane, R. H. Hardin, and W. D. Smith, "Tables of spherical codes." Published electronically at https://neilsloane.com/packings/ (2004), in collaboration with R. H. Hardin, W. D. Smith, and others
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N. J. A. Sloane, R. H. Hardin, and W. D. Smith, "Tables of spherical codes." Published electronically at https://neilsloane.com/packings/ (2004)
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Sole93:
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flm: >-
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P. Sole, "Generalized theta functions for lattice vector quantization", in Coding and Quantization, DIMACS Series in Dr,crete Mathenulies and Theoretical Computer Science, vol. 14. Providence, RH: American Math. Soc., 1993, pp. 27-32
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P. Sole, "Generalized theta functions for lattice vector quantization", in Coding and Quantization, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 14. Providence, RH: American Math. Soc., 1993, pp. 27-32
introduced: '\cite{doi:10.1016/S0019-9958(67)90835-2,manual:{N. V. Semakov and V. A. Zinovev, "Complete and Quasi-complete Balanced Codes", Problemy Peredachi Informatsii, 5:2 (1969), 14–18; Problems of Information Transmission, 5:2 (1969), 11–13}}'
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introduced: '\cite{doi:10.1016/S0019-9958(67)90835-2,manual:{N. V. Semakov and V. A. Zinoviev, "Complete and Quasi-complete Balanced Codes", Problemy Peredachi Informatsii, 5:2 (1969), 14–18; Problems of Information Transmission, 5:2 (1969), 11–13}}'
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alternative_names:
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- 'Semakov-Zinovev code'
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- 'Semakov-Zinoviev code'
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description: |
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A nonlinear \((16,256,6)\) binary code that is the smallest Kerdock code and the smallest Preparata code.
Copy file name to clipboardExpand all lines: codes/classical/properties/block/copyright/frameproof.yml
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A sufficient condition for an evaluation AG code to be FP can be recast as an instance of the Riemann-Roch equation \cite[Sec. 15.8.2]{preset:HKSag}.
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AG-based constructions of binary \((2,1)\)-separating systems can beat a random-coding lower bound \cite[Thm. 15.8.13]{preset:HKSag}.
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- code_id: kerdock
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detail: 'Kerdock codes of sufficient order are separating \cite{manual:{A. Krasnopeev and Yu. L. Sagalovich, "The Kerdock codes and separating systems." Eight International Workshop on Algebraic and Combinatorial Coding Theory. Vol. 7. No. 7.2. 2002},doi:10.1109/TIT.2004.838106}.'
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detail: 'Kerdock codes of sufficient order are separating \cite{manual:{A. Krasnopeev and Y. L. Sagalovich, "The Kerdock codes and separating systems," in Proc. 8th Int. Workshop on Algebraic and Combinatorial Coding Theory, Sept. 2002, pp. 165–167},doi:10.1109/TIT.2004.838106}.'
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# - code_id: traceability
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# detail: 'FP codes fingerprint digital data and also they help prevent copyrighted information from unauthorized use \cite{arxiv:1411.5782}.
Copy file name to clipboardExpand all lines: codes/classical/q-ary_digits/ag/evaluationAG/plane_curve.yml
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@@ -17,7 +17,7 @@ protection: 'Bezout''s theorem yields parameters \([n,k,d]\), which depend on th
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features:
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decoders:
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- 'Generalization of the Peterson algorithm for BCH codes \cite{doi:10.1109/18.32157,doi:10.1109/18.57204,manual:{V. Yu. Krachkovskii, "Decoding of codes on algebraic curves," (in Russian), Conference Odessa, 1988}}.'
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- 'Generalization of the Peterson algorithm for BCH codes \cite{doi:10.1109/18.32157,doi:10.1109/18.57204,manual:{V. Yu. Krachkovsky, (1988) "Decoding of codes on algebraic curves", Proceedings of the IX All-Union Conference on the Theory of Coding and Information Transmission, Moscow-Odessa: USSR Academy of Sciences, 1988 Part 2, pp. 143–146 (in Russian)}}.'
Copy file name to clipboardExpand all lines: codes/classical/q-ary_digits/packing/covering/covering.yml
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\end{align}
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A code is perfect iff it satisfies Eqs. \eqref{eq:perfect-ref} and \eqref{eq:spherepacking-perfect-label} with equality.
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In general, finding the covering radius of a code is \(NP\)-hard \cite{doi:10.1109/TIT.1984.1056978}. Complexity analysis as well as an extensive study of bounds can be found in Ref. \cite{manual:{G. Cohen, I. Honkala, S. Litsyn, and A. Lobstein, "Covering Codes", Elsevier (1997)}}.
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In general, finding the covering radius of a code is \(NP\)-hard \cite{doi:10.1109/TIT.1984.1056978}. Complexity analysis as well as an extensive study of bounds can be found in Ref. \cite{preset:CoveringBook}.
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realizations:
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- 'Data compression, both with and without distortion constraints, can be phrased in terms of covering codes \cite{manual:{G. Cohen, I. Honkala, S. Litsyn, and A. Lobstein, "Covering Codes", Elsevier (1997)}}.'
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- 'Data compression, both with and without distortion constraints, can be phrased in terms of covering codes \cite{preset:CoveringBook}.'
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- 'Football-pool problem: finding the smallest number of bets on a set of matches needed to guarantee at least one bet has at most \(\rho\) errors \cite{doi:10.2307/2974552,doi:10.1007/BF03025254}.'
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