NNMDS codes
A linear \([n,k,d]_q\) code is a subspace of dimension \(k\) in \(F_q^n\) with minimum Hamming distance \(q\). The Singleton bound gives that \(d \leq n-k+1.\) The Singleton defect is defined as \(s(C) = n+1-k-d.\) A code meeting the Singleton bound is known as a maximum distance separable (MDS) code. Codes with \(s(C)=s(C^\perp)=1\) are known as near maximum distance separable (NMDS) codes. The author extends this definition to study codes with \(s(C)=s(C^\perp)=2\), which the author calls NNMDS codes. The author gives an upper bound on the length of such codes and gives several necessary and sufficient conditions for their existence.
scientific article; zbMATH DE number 6134670