Abstract: According to research of cyclotomic cosets m, the property of cyclotomic cosets can be concluded when q>7 and m>1. The calculation formulae for period distribution of q-ary BCH codes with designed distance 9 are obtained based on the discussion of cyclotomic cosets and property of cyclotomic polynomials： the period distribution is q’s power. When the period is unequal to some special values, the power is the GCD of code-length and the period. When the period is special value, the power is n/b-m[8/b] , where n is the code-length, b is some number among 2 to 8 related to n and the period, and m is the index of q module n. The nonperiodic cyclic equivalence classes of this kind of codes can be counted due to the period distribution formula found and the Mobuis inverse.

Key words: BCH Codes, cyclotomic cosets, period distribution

摘要： 通过对循环陪集的进一步研究和讨论，得到当取q大于7，m大于1时有关循环陪集的一个性质，得到了设计距离为9的q元BCH码的周期分布的计算公式：码的周期分布为q的幂，当码的周期不等于某些特殊值时，幂为码长与周期的最大公因数。当码的周期为特殊值时，幂为n/b-m[8/b]，这里n是码的长度，b是由n和码的周期决定的2到8之间的整数，m是q模n的指数。由此计算公式和Mobius反转公式给出了无内周期码字个数的计数结果。

关键词: BCH码, 循环陪集, 周期分布