A MacWilliams-type identity for linear codes on weak order

Authors:
Dae San Kim;Jeh Gwon Lee
Affiliations:
Department of Mathematics, Sogang University, C.P.O. Box 1142, 121-742 Seoul, South Korea;Department of Mathematics, Sogang University, C.P.O. Box 1142, 121-742 Seoul, South Korea
Venue:
Discrete Mathematics
Year:
2003

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Abstract

Let P = n11 ⊕...⊕ nt1 be the poset given by the ordinal sum of the antichains ni1 with ni elements. Then we consider the P-weight enumerator for the linear code C of length n (n = n1+.... + nt) over Fq on P, and derive a MacWilliams-type identity relating the weight enumerator for the dual code C⊥ of C on P and that for C on the dual poset P of P. This generalizes the earlier work of Gutiérrez and Tapia-Recillas (Congr. Numer. 133 (1998) 63) corresponding to the case that t = 2, n1 = 1, n2 = n-1.