A class of imprimitive BCH codes and new quantum codes

Let q be a prime power, l ≥ 2 be even, n=(q-1)(q^il-1)/(qⁱ-1). We give necessary and sufficient conditions on dual containing q-ary narrow-sense BCH codes of length ⁿ, and improve previous upper bound on necessary condition. We present a family of dual containing non-narrow-sense BCH codes of length ⁿ including the BCH code with maximal designed distance, calculate their dimensions and use them to construct new quantum codes, which are better than those constructed from narrow-sense BCH codes.