Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes
Information Theory
2024-12-19 v1 math.IT
Abstract
This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both matrix and polynomial approaches. We provide two versions of necessary and sufficient conditions for two-generator quasi-cyclic codes for symplectic self-orthogonality and the symplectic dual-containing condition. Additionally, using these necessary and sufficient conditions, we construct new quantum codes with record-breaking parameters that improve upon current records.
Cite
@article{arxiv.2412.13613,
title = {Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes},
author = {Tushar Bag and Hai Q Dinh and Daniel Panario},
journal= {arXiv preprint arXiv:2412.13613},
year = {2024}
}