The maximum designed distances of dual-containing non-primitive BCH codes

Let q be a prime power and m a positive integer. Suppose that a >= 2 is a factor of qm - 1 such that m is the multiplicative order of q modulo n := qm-1 a . Firstly, for m odd and m even, we present some necessary and sufficient conditions on dual -containing non -primitive BCH codes of length n with the maximum designed distances over Fq, respectively. The results show that the maximum designed distances of dual -containing BCH codes in this paper are larger than those in [2, Theorem 3]. Secondly, we explicitly determine the dimensions of some dual -containing non -primitive BCH codes of length n, and finally, we construct some new quantum codes with relatively large minimum distances. (c) 2024 Elsevier B.V. All rights reserved.