A MacWilliams-type identity for linear codes on weak order

摘要

Let P = n_l1?…?n_t1 be the poset given by the ordinal sum of the antichains n_i1 with n_i elements. Then we consider the P-weight enumerator for the linear code C of length n (n = n_1 +…+ n_t) over F_q 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 Gutierrez and Tapia-Recillas (Congr. Numer. 133 (1998) 63) corresponding to the case that t = 2, n_1 = 1, n_2 = n - 1.