设计距离为7的q元BCH码的周期分布

Period Distributions of q-ary BCH Codes with Designed Distance 7

通过对循环陪集的研究及利用分圆多项式的一个性质,得到了设计距离为7的q元BCH码的周期分布计算公式: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[6/b],这里n是码的长度,b是由n和码的周期决定的2到6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.

The calculation formulae for period distribution of q-ary BCH codes with designed distance 7 were obtained based on the discussion of cyclotomic cosets and property of cyclotomic polynomials： the period distribution is q＇s power. When the period was unequal to some special values, the power was the GCD of code-length and the period. When the period was of special value, the power was n[b - m [6/b] ; where n was the codelength, b was some number among 2 to 6 related to n and the period, and m was the index of q module n. The nonperiodic cyclic equivalence classes of this kind of codes could be counted due to the period distribution formula and the Mobuis inverse formula.