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  • Yonglin Cao
  • 2011
For R a Galois ring and m 1, . . . , m l positive integers, a generalized quasi-cyclic (GQC) code over R of block lengths (m 1, m 2, . . . , m l ) and length $${\sum_{i=1}^lm_i}$$ is an R[x]-submodule of $${R[x]/(x^{m_1}-1)\times\cdots \times R[x]/(x^{m_l}-1)}$$ . Suppose m 1, . . . , m l are all coprime to the characteristic of R and let {g 1, . . . , g t(More)
  • Yonglin Cao
  • 2012
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)
In this paper, we study the construction of cyclic DNA codes by cyclic codes over the finite chain ring     2 4 1 F u u . First, we establish a 1-1 correspondence  between DNA pairs and the 16 elements of the ring     2 4 1 F u u . Considering the biology features of DNA codes, we investigate the structure and properties of self-reciprocal(More)
Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $R=\mathbb{F}_{p^m}[u]/\langle u^2\rangle=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ $(u^2=0)$, where $p$ is a prime and $m$ is a positive integer. For any $\lambda\in \mathbb{F}_{p^m}^{\times}$, an explicit representation for all distinct $\lambda$-constacyclic codes over $R$ of length $p^sn$ is(More)