Skew Cyclic Codes Over F_4 R

12/27/2018

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by   Nasreddine Benbelkacem, et al.

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This paper considers a new alphabet set, which is a ring that we call F_4R, to construct linear error-control codes. Skew cyclic codes over the ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize F_4R-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over F_4 are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of R-skew cyclic codes which are reversible complement.