A MacWilliams-type identity for linear codes on weak order Original Research Article

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 P̌ 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.