@Article{CSIAM-AM-4-1,
author = {Zicheng, Ye and Zhang, Huazi and Rong, Li and Wang, Jun and Yan, Guiying and Zhiming, Ma},
title = {Improving the Gilbert-Varshamov Bound by Graph Spectral Method},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2023},
volume = {4},
number = {1},
pages = {1--12},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2708-0579},
doi = {https://doi.org/ 10.4208/csiam-am.SO-2021-0024},
url = {https://global-sci.com/article/82280/improving-the-gilbert-varshamov-bound-by-graph-spectral-method}
}