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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)
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)
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)