Open AccessAdditive polycyclic codes over $ \mathbb{F}_{4} $ induced by binary vectors and some optimal codes
Author(s) -
Arezoo Soufi Karbaski,
Taher Abualrub,
Nuh Aydın,
Peihan Liu
Publication year - 2024
Publication title -
advances in mathematics of communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.601
H-Index - 26
eISSN - 1930-5346
pISSN - 1930-5338
DOI - 10.3934/amc.2022004
Subject(s) - mathematics , cardinality (data modeling) , dual polyhedron , combinatorics , binary number , discrete mathematics , generator matrix , generator (circuit theory) , code (set theory) , arithmetic , physics , algorithm , computer science , power (physics) , decoding methods , set (abstract data type) , quantum mechanics , data mining , programming language
In this paper, we study the structure and properties of additive right and left polycyclic codes induced by a binary vector \begin{document}$ a $\end{document} in \begin{document}$ \mathbb{F}_{2}^{n}. $\end{document} We find the generator polynomials and the cardinality of these codes. We also study different duals for these codes. In particular, we show that if \begin{document}$ C $\end{document} is a right polycyclic code induced by a vector \begin{document}$ a\in \mathbb{F}_{2}^{n} $\end{document} , then the Hermitian dual of \begin{document}$ C $\end{document} is a sequential code induced by \begin{document}$ a. $\end{document} As an application of these codes, we present examples of additive right polycyclic codes over \begin{document}$ \mathbb{F}_{4} $\end{document} with more codewords than comparable optimal linear codes as well as optimal binary linear codes and optimal quantum codes obtained from additive right polycyclic codes over \begin{document}$ \mathbb{F}_{4}. $\end{document}