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In this paper, we consider the construction of linear lexicodes over finite chain rings by using a Bordering over these rings and a selection criterion. As examples we give lexicodes over Z 4 and F 2 + uF 2. It is shown that this construction produces many optimal codes over rings and also good binary codes. Some of these codes meet the Gilbert bound. We… (More)

In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal… (More)

—In this paper we investigate repeated root cyclic and negacyclic codes of length p r m over Fps with (m, p) = 1. In the case p odd, we give necessary and sufficient conditions on the existence of negacyclic self-dual codes. When m = 2m ′ with m ′ odd, we characterize the codes in terms of their generator polynomials. This provides simple conditions on the… (More)

This paper considers cyclic DNA codes of arbitrary length over the ring R = F 2 [u]/u 4 − 1. A mapping is given between the elements of R and the alphabet {A, C, G, T } which allows the additive stem distance to be extended to this ring. Cyclic codes over R are designed such that their images under the mapping are also cyclic or quasi-cyclic of index 2. The… (More)

This paper is dealing with DNA cyclic codes which play an important role in DNA computing and have attracted a particular attention in the literature. Firstly, we introduce a new family of DNA cyclic codes over the ring R = F2[u]/(u 6). Such codes have theoretical advantages as well as several applications in DNA computing. A direct link between the… (More)

We construct codes over the ring F 2 +uF 2 with u 2 = 0. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the GC content constraint and avoid the secondary structure. they are derived from the cyclic complement reversible codes over the ring F 2 + uF 2. We also construct an infinite… (More)

For λ an n-th power of a unit in a finite chain ring we prove that λ-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the α+pβ-constacyclic codes of length p s over the Galois ring GR(p e , r).

We construct codes over the ring $$\mathbb F _2+u\mathbb F _2$$ F 2 + u F 2 with $$u^2=0$$ u 2 = 0 for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $$GC$$ G C content constraint, and avoid the secondary structure. They are derived from cyclic reverse-complement codes over the ring $$\mathbb F… (More)

The asymmetric CSS construction is extended to the Hermitian case. New infinite families of quantum symmetric and asymmetric codes are constructed. The codes obtained are shown to have parameters better than those of previous codes. A number of known codes are special cases of the codes given here.