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1996-01

A Characterization of Codes with Extreme Parameters

by Faldum, A., Willems, W..


Series: 1996-01, Preprints

MSC:
94B05 Linear codes, general

Abstract:
Let C be an [n; k; d]-code over GF (q) with k >= 2. Let s =
def (C) = n + 1 - k - d denote the defect of C. The Griesmer bound implies
that d <= q (s + 1). If d > qs and s >= 2, then by previous results of the authors,
k <= q. Thus fixing s >= 2 the extreme parameters for a code with def (C) = s are
d = q (s + 1), k = q and n = k + d + s - 1 = (q + 1) (s + 2) - 3. In this note we
characterize the codes with such parameters.


Keywords:

This paper was published in:
IEEE Trans. Inf. Theory 42, No.6, Pt.2, 2255-2257 (1996)