关键词: BCH码, 循环陪集, 周期分布

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