Additive Polycyclic Codes over $\mathbb{F}_{4}$ Induced by Binary Vectors and Some Optimal Codes
Information Theory
2021-08-23 v1 math.IT
Abstract
In this paper we study the structure and properties of additive right and left polycyclic codes induced by a binary vector in 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 is a right polycyclic code induced by a vector , then the Hermitian dual of is a sequential code induced by As an application of these codes, we present examples of additive right polycyclic codes over 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
Keywords
Cite
@article{arxiv.2108.09198,
title = {Additive Polycyclic Codes over $\mathbb{F}_{4}$ Induced by Binary Vectors and Some Optimal Codes},
author = {Arezoo Soufi Karbaski and Taher Abualrub and Nuh Aydin and Peihan Liu},
journal= {arXiv preprint arXiv:2108.09198},
year = {2021}
}