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arXiv · 2108.09198

Additive Polycyclic Codes over $\mathbb{F}_{4}$ Induced by Binary Vectors and Some Optimal Codes

Arezoo Soufi Karbaski·Taher Abualrub·Nuh Aydin·Peihan Liu
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Abstract

In this paper we study the structure and properties of additive right and left polycyclic codes induced by a binary vector $a$ in $\mathbb{F}_{2}^{n}.$ We find the generator polynomials and the cardinality of these codes. We also study different duals for these codes. In particular, we show that if $C$ is a right polycyclic code induced by a vector $a\in \mathbb{F}_{2}^{n}$, then the Hermitian dual of $C$ is a sequential code induced by $a.$ As an application of these codes, we present examples of additive right polycyclic codes over $\mathbb{F}_{4}$ with more codewords than comparable optimal linear codes as well as optimal binary linear codes and optimal quantum codes obtained from additive right polycyclic codes over $\mathbb{F}_{4}.$

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Arezoo Soufi Karbaski, Taher Abualrub, Nuh Aydin, Peihan Liu. 2021-08-20. Additive Polycyclic Codes over $\mathbb{F}_{4}$ Induced by Binary Vectors and Some Optimal Codes. https://arxiv.org/abs/2108.09198

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