Yonglin Cao

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Let R be an arbitrary commutative finite chain ring with $$1\ne 0$$ . 1-generator quasi-cyclic (QC) codes over R are considered in this paper. Let $$\gamma $$ be a fixed generator of the maximal ideal of R, $$F=R/\langle \gamma \rangle $$ and $$|F|=q$$ . For any positive integers m, n satisfying $$\mathrm{gcd}(q,n)=1$$ , let $$\mathcal{R}_n=R[x]/\langle(More)
Keywords: Additive cyclic code Galois ring Linear code Dual code Trace inner product Self-dual code Quasi-cyclic code a b s t r a c t Let R = GR(p ϵ , l) be a Galois ring of characteristic p ϵ and cardinality p ϵl , where p and l are prime integers. First, we give a canonical form decomposition for additive cyclic codes over R. This decomposition is used to(More)