On the weight hierarchy of the semiprimitive codes

Abstract

An irreducible cyclic (n, k) code is said to be semiprimitive if n = (2^k − 1)/N where N > 2 divides 2^j + 1 for some j ≥ 1. The complete weight hierarchy of the semiprimitive codes is determined when k/2j is odd. In the other cases, when k/2j is even, some partial results on the generalized Hamming weights of the semiprimitive codes are obtained. We apply the above results to find the generalized Hamming weight of some classes of dual codes of primitive BCH codes with designed distance N + 2 when k/2j is odd.