Abstract
By a careful analysis on cyclotomic cosets, the maximal designed distance δnew of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length [Formula: see text] is determined, where q is a prime power and l is odd. Our maximal designed distance δnew of dual containing narrow-sense BCH codes of length n improves upon the lower bound δmax for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δnew, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.
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