Abstract
Let q be a prime power and m ≥ 4 an even integer. Suppose that n = q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m-1</sup> /a such that m is the multiplicative order of q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> modulo n, where a ≥ 2 is a positive integer. This letter mainly determines the maximum designed distance of Hermitian dual-containing Bose-Chaudhuri-Hocquenghem (BCH) codes of length n over F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q2</sub> . Our results show that the designed distances of non-primitive BCH codes in this letter are larger. Moreover, we obtain the dimensions of some non-primitive BCH codes.
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