Reversible Codes and Its Application to Reversible DNA Codes over F_4^k

06/12/2018

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by   Lei Chen, et al.

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Coterm polynomials are introduced by Oztas et al. [a novel approach for constructing reversible codes and applications to DNA codes over the ring F_2[u]/(u^2k-1), Finite Fields and Their Applications 46 (2017).pp. 217-234.], which generate reversible codes. In this paper, we generalize the coterm polynomials and construct some reversible codes which are optimal codes by using m-quasi-reciprocal polynomials. Moreover, we give a map from DNA k-bases to the elements of F_4^k, and construct reversible DNA codes over F_4^k by DNA-m-quasi-reciprocal polynomials.