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NMDS codes of maximal length over Fq,8⩽q⩽11

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3 Author(s)
Marcugini, S. ; Dept. of Math. & Informatics, Perugia Univ., Italy ; Milani, A. ; Pambianco, F.

A linear [n,k,d]q code C is called near maximum-distance separable (NMDS) if d(C)=n-k and d(C)=k. The maximum length of an NMDS [n,k,d]q code is denoted by m'(k,q). In this correspondence, it has been verified by a computer-based proof that m'(5,8)=15, m'(4,9)=16,m'(5,9)=16, and 20⩽m'(4,11)⩽21. Moreover, the NMDS codes of length m'(4,8), m'(5,8), and m'(4,9) have been classified. As the dual code of an NMDS code is NMDS, the values of m'(k,8), k=10,11,12, and of m'(k,9),k=12,13,14 have been also deduced

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 4 )