Linear $\ell$-Intersection Pairs of Codes and Their Applications
Information Theory
2019-07-09 v2 math.IT
Abstract
In this paper, a linear -intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear -intersection pair if their intersection has dimension . Characterizations and constructions of such pairs of codes are given in terms of the corresponding generator and parity-check matrices. Linear -intersection pairs of MDS codes over of length up to are given for all possible parameters. As an application, linear -intersection pairs of codes are used to construct entanglement-assisted quantum error correcting codes. This provides a large number of new MDS entanglement-assisted quantum error correcting codes.
Cite
@article{arxiv.1810.05103,
title = {Linear $\ell$-Intersection Pairs of Codes and Their Applications},
author = {Kenza Guenda and T. Aaron Gulliver and Somphong Jitman and Satanan Thipworawimon},
journal= {arXiv preprint arXiv:1810.05103},
year = {2019}
}