The Period Distribution And Depth Spectrum For Cyclic Codes

Let q be a power of the prime p and Fq the q elements finite field. In this thesis, we study the period distribution and the depth spectrum for cyclic codes over Fq. By using cyclotomic cosets tool, the precise formula of the period distribution for a q-ary BCH code over Fq with designed distanceδ(2≤δ≤T+1, T is the maximal non-repeated bound of a cyclotomic coset) and its dual code are given. Furthermore, we study the structure of the cyclic code C over the ring R=Fq+uFq(u2=0),and obtain the period distribution and depth spectrum for C...