Additive Polycyclic Codes over 𝔽_4 Induced by Binary Vectors and Some Optimal Codes

08/20/2021

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by   Arezoo Soufi Karbaski, et al.

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In this paper we study the structure and properties of additive right and left polycyclic codes induced by a binary vector a in 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∈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 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 𝔽_4.