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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), pp. 3-44 \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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flm: >-
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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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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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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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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), pp. 79-96 \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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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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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), pp. 111-128 \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), pp. 385-428 \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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# flm: >-
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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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# 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), pp. 151-180 \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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# 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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# 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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# 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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# 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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# flm: >-
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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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# 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), pp. 251-266 \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), pp. 763-784 \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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# 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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# 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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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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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), pp. 311-362 \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), pp. 363-384 \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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# 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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# 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), pp. 449-462 \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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# 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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# 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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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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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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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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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), pp. 575-598 \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), pp. 645-656 \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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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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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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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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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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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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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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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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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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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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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), pp. 599-612 \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), pp. 613-644 \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), pp. 785-798 \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), pp. 799-822 \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}
Higher-dimensional lattices yield quantizers with lower normalized second moments than the 1D integer lattice \cite{manual:{P. L. Zador, Development and evaluation of procedures for quantizing multivariate distributions, PhD thesis, Stanford Univ., 1963},doi:10.1109/TIT.1982.1056490}.
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Higher-dimensional lattices yield quantizers with lower normalized second moments than the 1D integer lattice \cite{manual:{P. L. Zador, Development and evaluation of procedures for quantizing multivariate distributions, PhD thesis, Stanford University, 1963},doi:10.1109/TIT.1982.1056490}.
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The \textit{shortest vector problem} (SVP) asks for the shortest nonzero vector in a given lattice and is related to cryptographic protocols.
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Solving SVP up to an error independent of lattice dimension is NP-complete \cite{manual:{P. van Emde Boas, "Another NP-complete problem and the complexity of computing short vectors in a lattice," Technical Report, Department of Mathematics, University of Amsterdam (1981)},doi:10.1137/S0097539700373039}.
@@ -63,7 +63,7 @@ protection: |
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rate: |
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Lattices with minimal-distance decoding achieve the capacity of the AWGN channel \cite{doi:10.1109/18.651040,doi:10.1109/TIT.1975.1055409,manual:{R. de Buda and W. Kassem, About lattices and the random coding theorem, in Abstracts of Papers, IEEE Inter. Symp. Info. Theory 1981, IEEE Press, NY 1981, p. 145},manual:{W. Kassem, Optimal Lattice Codes for the Gaussian Channel, PhD thesis, McMaster Univ., Hamilton, Ontario, 1981,doi:10.1109/18.651040}}.
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Lattices with minimal-distance decoding achieve the capacity of the AWGN channel \cite{doi:10.1109/18.651040,doi:10.1109/TIT.1975.1055409,manual:{R. de Buda and W. Kassem, About lattices and the random coding theorem, in Abstracts of Papers, IEEE Inter. Symp. Info. Theory 1981, IEEE Press, NY 1981, p. 145},manual:{W. Kassem, Optimal Lattice Codes for the Gaussian Channel, PhD thesis, McMaster University, Hamilton, Ontario, 1981}}.
Copy file name to clipboardExpand all lines: codes/classical/properties/block/symmetry/cyclic/quasi_cyclic.yml
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- code_id: self_dual
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detail: 'Quasi-cyclic self-dual constructions include double circulant codes and, in odd characteristic, their negacirculant analogs such as double negacirculant and four-negacirculant codes \cite[Sec. 4.4]{preset:HKSselfdual}.'
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- code_id: convolutional
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detail: 'Quasi-cyclic codes can be \textit{unwrapped} to obtain convolutional codes \cite{manual:{G. D. Forney, Jr., "Why quasi cyclic codes are interesting," unpublished note, 1970},doi:10.1137/0137027,manual:{R. M. Tanner, ERROR-CORRECTING CODING SYSTEM, U.S. Patent 4295218, 1981},manual:{R. M. Tanner. Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes. University of California, Santa Cruz, Computer Research Laboratory, 1987},manual:{H. H. Ma, "Generalized tail-biting convolutional codes," PhD thesis, Univ. of Massachusetts, Amherst, 1985},manual:{Y. Levy and J. Costello, Jr., "An algebraic approach to constructing convolutional codes from quasi-cyclic codes," DIMACS Ser. Discr. Math. and Theor. Comp. Sci., vol. 14, pp. 189–198, 1993},doi:10.1109/18.651076}.'
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detail: 'Quasi-cyclic codes can be \textit{unwrapped} to obtain convolutional codes \cite{manual:{G. D. Forney, Jr., "Why quasi cyclic codes are interesting," unpublished note, 1970},doi:10.1137/0137027,manual:{R. M. Tanner, ERROR-CORRECTING CODING SYSTEM, U.S. Patent 4295218, 1981},manual:{R. M. Tanner. Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes. University of California, Santa Cruz, Computer Research Laboratory, 1987},manual:{H. H. Ma, "Generalized tail-biting convolutional codes," PhD thesis, University of Massachusetts, Amherst, 1985},manual:{Y. Levy and J. Costello, Jr., "An algebraic approach to constructing convolutional codes from quasi-cyclic codes," DIMACS Ser. Discr. Math. and Theor. Comp. Sci., vol. 14, pp. 189–198, 1993},doi:10.1109/18.651076}.'
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- code_id: sc_qldpc
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detail: 'Quasi-cyclic binary code parity-check matrices can be used as sub-matrices to define a 1D SC-QLDPC code \cite{arxiv:1102.3181}.'
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