New distance bounds for one-generator quasi-cyclic codes with applications to Hermitian LCD codes and entanglement-assisted quantum codes
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Abdukhalikov, Kanat, Ho, Duy, Shat, Rasha M.
Institution: United Arab Emirates University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: United Arab Emirates University
Award: G5271242052
OpenAlex ID: W7214667622