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  • Yonglin Cao
  • Applicable Algebra in Engineering, Communication…
  • 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
  • Applicable Algebra in Engineering, Communication…
  • 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)
Let R = GR(p, l) be a Galois ring of characteristic p and cardinality pεl, 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 construct additive cyclic codes and count the number of such codes, respectively. Thenwe give the trace dual code for each additive cyclic(More)
Let Fpm be a finite field of cardinality p m and R = Fpm[u]/〈u 〉 = Fpm +uFpm (u = 0), where p is a prime and m is a positive integer. For any λ ∈ Fpm, an explicit representation for all distinct λ-constacyclic codes over R of length pn is given by a canonical form decomposition for each code, where s and n are positive integers satisfying gcd(p, n) = 1. For(More)
Let Fq be a finite field of cardinality q , l a prime number and Fql an extension field of Fq with degree l. The structure and canonical form decompositions of semisimple multivariable Fq -linear codes over Fql are presented. Enumeration and construction of these codes are then investigated. Especially, dual codes, self-orthogonality and self-duality of(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 selfreciprocal(More)