Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of BCH codes, there are relatively little study on constacyclic BCH codes. The objective of this paper is to determine the dimension and minimum distance of a class of q-ary constacyclic BCH codes of length \(\frac {q^{m}-1}{q-1}\) with designed distances \(\delta _{i}=q^{m-1}-\frac {q^{\lfloor \frac {m-3}2 \rfloor +i }-1}{q-1}\) for \(1\leq i\leq \min \limits \{\lceil \frac {m+1}2 \rceil -\lfloor \frac {m}{q+1} \rfloor , \lceil \frac {m-1}2 \rceil \}\). As will be seen, some of these codes are optimal.

中文翻译：

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一类常量BCH码

恒定码是线性码的一个子类，并且已经得到了很好的研究。并发BCH代码是并发代码系列，并且包含BCH代码作为子类。与对BCH码的深入研究相比，对固定BCH码的研究相对较少。本文的目的是确定具有设计距离\（\ frac {q ^ {m} -1} {q-1} \）的一类q元稳定BCH码的尺寸和最小距离。\增量_ {I} = q ^ {M-1} - \压裂{q ^ {\ lfloor \压裂{M-3} 2 \ rfloor + I} -1} {q-1} \）为\（1 \ leq i \ leq \ min \ limits \ {\ lceil \ frac {m + 1} 2 \ rceil-\ lfloor \ frac {m} {q + 1} \ rfloor，\ lceil \ frac {m-1} 2 \ rceil \} \）。可以看出，其中一些代码是最佳的。