Better error correction codes improve quantum and classical communications
New distance bounds for one-generator quasi-cyclic codes with applications to Hermitian LCD codes and entanglement-assisted quantum codes
Information Theory
Summary
The paper finds new ways to measure how well certain error-correcting codes called one-generator quasi-cyclic codes can detect mistakes when data is sent. These new measurements help find codes that work better than older ones. The authors used these codes to create special codes that help protect quantum information from errors. These improved codes could lead to better data and quantum communication technologies.
What this means in practice
- •For quantum communication engineers: Use improved quantum error-correcting codes to protect quantum data transmissions with higher entanglement efficiency.
- •For digital communication specialists: Implement new minimum distance bounds to design more reliable classical error-correcting codes for data storage and transmission.
Authors
Kanat Abdukhalikov, Duy Ho, Rasha M. Shat
Abstract
We introduce lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index, obtained by puncturing and shortening the code at the level of its blocks. For balanced codes, these bounds form a nondecreasing chain whose first term is the Jensen bound. We apply these bounds to conduct a computer search and obtain many Hermitian LCD codes with good parameters. Among them there are six codes of length at most 30 which improve the corresponding lower bounds of Araya and Harada. These codes further give maximal-entanglement entanglement-assisted quantum codes, which we compare with the parameters currently recorded in the literature.