Let $q$ be a prime power and $m\ge 4$ an even integer. Suppose that $n = \frac {q^{2m}-1}a$ such that $m$ is the multiplicative order of $q^{2}$ modulo $n$ , where $a\ge 2$ 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 $\Bbb F_{q^{2}}$ . 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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埃尔米特对偶包含非原始BCH码

让 $ q $ 成为主要力量 $ m \ ge 4 $ 一个偶数整数。假设 $ n = \ frac {q ^ {2m} -1} a $ 这样 $ m $ 是...的乘法阶 $ q ^ {2} $ 模数 $ n $ ， 在哪里 $ a \ ge 2 $ 是一个正整数。该字母主要确定长度为Hermitian的含双重Bose-Chaudhuri-Hocquenghem（BCH）码的最大设计距离 $ n $ 超过 $ \ Bbb F_ {q ^ {2}} $ 。我们的结果表明，该字母中非原始BCH码的设计距离更大。此外，我们获得了一些非原始BCH码的维数。