Learn More
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)
This paper considers cyclic DNA codes of arbitrary length over the ring R = F<sub>2</sub>[u]/(u<sup>4</sup> - 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. Then, cyclic codes over R are designed such that their images under the mapping are also cyclic or(More)
In this paper we investigate repeated root cyclic and negacyclic codes of length p<sup>r</sup> m over F<sub>ps</sub> 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(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)
Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared entanglement between the sender and receiver. However, in general it is not easy to determine the number of shared pairs(More)