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arXiv · 1812.10692

Skew Cyclic Codes Over $\mathbb{F}_4 R$

Nasreddine Benbelkacem·Martianus Frederic Ezerman·Taher Abualrub·Aicha Batoul
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Abstract

This paper considers a new alphabet set, which is a ring that we call $\mathbb{F}_4R$, 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 $\mathbb{F}_4R$-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over $\mathbb{F}_4$ 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.

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Nasreddine Benbelkacem, Martianus Frederic Ezerman, Taher Abualrub, Aicha Batoul. 2018-12-27. Skew Cyclic Codes Over $\mathbb{F}_4 R$. https://doi.org/10.1142/s0219498822500657

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