设计距离为9的q元BCH码的周期分布

Period distributions of q-ary BCH codes with designed distance 9

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。

According to research of cyclotomic cosets m, the property of cyclotomic cosetscan be concluded when q〉7 and m〉l. The calculation formulae for period distribution of q-ary BCH codes with designed distance 9 are obtained based on the discussion of cyclo tomic 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.