DNA Images of Codes Over F4t [u]/&lt;uk&gt;

doi:10.21203/rs.3.rs-2966940/v1

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Research Article

DNA Images of Codes Over F₄^_t [u]/<u^k>

https://doi.org/10.21203/rs.3.rs-2966940/v1

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The aim of this paper is to study DNA codes using some Gray images of codes over the chain rings S = F₄^_t [u]<u^k> and R = F₄[v]⁄<v^tk>. The special cases t=1 and k=2,3 were studied before. We construct some nice Gray maps from R, S to DNA codewords, whose images satisfy complement and reversibility properties. Studying the general case allows us to construct codes with better parameters. Subsequently, we concentrate on codes over arbitrary commutative rings and cyclic codes over R and obtain some necessary and sufficient conditions equal to the common constraints on DNA codes, like reversibility. Moreover, a variety of sample codes over multiple rings are presented.

MSC Classification: 11T71 , 94B05 , 94B15

Algebra

Applied Mathematics

DNA Codes

Reversible Codes

Watson-Crick Complement

Cyclic Codes

Chain Rings

Local Rings