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Author: valbert4

codes/classical/q-ary_digits/distributed_storage/mds.yml

@@ -24,7 +24,7 @@ description: |
   A bound for general (i.e., nonlinear or unrestricted) \(q\)-ary codes can also be formulated; see \cite[Thm. 1.9.10]{preset:HKSbasics}.
   A code is \textit{near MDS} (NMDS) if both the code and its dual are AMDS.
 
-  The codes \( [n,1,n]_q, [n,n-1,2]_q, [n,n,1]_q \) for any \(q\) are MDS codes. These are called the \textit{trivial} MDS codes \cite[Sec. 3.3.2]{preset:HKSclass}. The only binary MDS codes are the trivial ones.
+  The codes \( [n,1,n]_q, [n,n-1,2]_q, [n,n]_q \) for any \(q\) are MDS codes. These are called the \textit{trivial} MDS codes \cite[Sec. 3.3.2]{preset:HKSclass}. The only binary MDS codes are the trivial ones.
   Many, but not all, \(q\)-ary MDS codes are related to RS codes and their extensions; see, e.g., \cite[Prob. 11.11]{doi:10.1017/CBO9780511808968}.
 
 

codes/classical/q-ary_digits/q-ary_linear.yml

@@ -43,7 +43,7 @@ features:
 # The best information set decoding algorithms have an average time complexity of exponential time - approximately \(n^{3}2^{n}\).
 
 notes:
-  - 'The two extreme examples of codes are the \([n,0,n]_q\) \textit{zero code} and its dual the \([n,n,1]_q\) \textit{universe code}.'
+  - 'The two extreme examples of codes are the \([n,0,n]_q\) \textit{zero code} and its dual the \([n,n]_q\) \textit{universe code}.'
   - 'University of Salzburg''s \href{https://web.archive.org/web/20221213223211/http://mint.sbg.ac.at/table.php?i=c}{MinT application} generates an optimal parameter table for a linear code \([n,k,d]_q\), contingent on an optional fluctuation of maximal Hamming code distance, rank, and length, along with other specifications.'
   - 'CodingTheory Julia software library \cite{preset:Sabo}.'