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- W4297797905 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 $ain mathbb{F}_{2}^{n}$, 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 $mathbb{F}_{4}.$" @default.
- W4297797905 created "2022-10-01" @default.
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- W4297797905 date "2021-08-20" @default.
- W4297797905 modified "2023-09-30" @default.
- W4297797905 title "Additive Polycyclic Codes over $mathbb{F}_{4}$ Induced by Binary Vectors and Some Optimal Codes" @default.
- W4297797905 doi "https://doi.org/10.48550/arxiv.2108.09198" @default.
- W4297797905 hasPublicationYear "2021" @default.
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