Period Distributions of q-ary BCH Codes with Designed Distance 7
Xiaosong Chen · Journal of Hunan University · 2007
According to research of cyclotomic cosets m,the property of cyclotomic cosets can be concluded when q7 and m1. 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.