Year: 2023
Author: Zicheng Ye, Huazi Zhang, Rong Li, Jun Wang, Guiying Yan, Zhiming Ma
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 1 : pp. 1–12
Abstract
We improve Gilbert-Varshamov bound by graph spectral method. Gilbert graph $G_{q,n,d}$ is a graph with all vectors in $\mathbb{F}^n_q$ as vertices where two vertices are adjacent if their Hamming distance is less than $d.$ In this paper, we calculate the eigenvalues and eigenvectors of $G_{q,n,d}$ using the properties of Cayley graph. The improved bound is associated with the minimum eigenvalue of the graph. Finally we give an algorithm to calculate the bound and linear codes which satisfy the bound.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0024
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 1 : pp. 1–12
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Gilbert–Varshamov bound independence number graph spectral method Cayley graph linear codes.