In this paper, we study polycyclic codes over the ring $ R_l = \frac{\mathbb{F}_q[w]}{\langle w^l - 1 \rangle} $ with $ q = p^k $ where $ k $ is a positive integer and $ p $ is an odd prime. We explore LCD annihilator, self-dual, self-orthogonal codes over $ R_l $ and polycyclic codes over $ R_l $. Moreover, we provide a structure of entanglement-assisted quantum error-correcting codes based on the developed polycyclic codes through the inclusion of dual contained conditions. Subsequently, some LCD hull code-derived entanglement-assisted quantum error-correcting code examples are presented.Accepted: 16 March 2026

Journal of Algebra Combinatorics Discrete Structures and ApplicationsMay 6, 20260 citations

arXiv:1610.04013

Entanglement-Assisted Quantum Error-Correcting Codes

Todd A. Brun, Min-Hsiu Hsieh

Published Oct 13, 2016• 0 citations

arXiv HTML PDF

Abstract

We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.

DOI: 10.48550/arxiv.1610.04013

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EAQEC codes from polycyclic codes over the ring

R_l

In this paper, we study polycyclic codes over the ring

R_l = \frac{\mathbb{F}_q[w]}{\langle w^l - 1 \rangle}

with

q = p^k

where

k

is a positive integer and

p

is an odd prime. We explore LCD annihilator, self-dual, self-orthogonal codes over

R_l

and polycyclic codes over

R_l

. Moreover, we provide a structure of entanglement-assisted quantum error-correcting codes based on the developed polycyclic codes through the inclusion of dual contained conditions. Subsequently, some LCD hull code-derived entanglement-assisted quantum error-correcting code examples are presented.Accepted: 16 March 2026