On the $\ell$-DLIPs of codes over finite commutative rings
Abstract
Generalizing the linear complementary duals, the linear complementary pairs and the hull of codes, we introduce the concept of -dimension linear intersection pairs (-DLIPs) of codes over a finite commutative ring , for some positive integer . In this paper, we study -DLIP of codes over in a very general setting by a uniform method. Besides, we provide a necessary and sufficient condition for the existence of a non-free (or free) -DLIP of codes over a finite commutative Frobenius ring. In addition, we obtain a generator set of the intersection of two constacyclic codes over a finite chain ring, which helps us to get an important characterization of -DLIP of constacyclic codes. Finally, the -DLIP of constacyclic codes over a finite chain ring are used to construct new entanglement-assisted quantum error correcting (EAQEC) codes.
Keywords
Cite
@article{arxiv.2204.00905,
title = {On the $\ell$-DLIPs of codes over finite commutative rings},
author = {Sanjit Bhowmick and Alexandre Fotue Tabue and Joydeb Pal},
journal= {arXiv preprint arXiv:2204.00905},
year = {2023}
}