A linear [n, k, d](q) code C is called near maximum-distance separable (NMDS) if d(C) = n - k and d(C-perpendicular to) = 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'(51 9) == 16, and 20 less than or equal to m'(4, 11) less than or equal to 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.
NMDS codes of maximal length over GF(q), 8<=q<=11
MARCUGINI, Stefano;MILANI, Alfredo;PAMBIANCO, Fernanda
2002
Abstract
A linear [n, k, d](q) code C is called near maximum-distance separable (NMDS) if d(C) = n - k and d(C-perpendicular to) = 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'(51 9) == 16, and 20 less than or equal to m'(4, 11) less than or equal to 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.File in questo prodotto:
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