A MacWilliams-type identity for linear codes on weak order

Dae San Kim, Jeh Gwon Lee
2003 Discrete Mathematics  
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 Gutià errez and Tapia-Recillas (Congr. Numer. 133 (1998) 63) corresponding to the case that t = 2, n1 = 1, n2 = n − 1.
doi:10.1016/s0012-365x(02)00498-3 fatcat:2lzopoqhqbfcdget5iongh4rv4