Abstract:This paper improves Gilbert-Varshamov bound by graph spectral method. Gilbert graph Gq,n,d is a graph with all vectors in Fnq 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 Gq,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.
Publication:CSIAM Trans. Appl. Math. Vol. 4, No. 1, pp. 1-12，2023
Author:Zicheng Ye1(2), Huazi Zhang(3), Rong Li(3), Jun Wang(3), Guiying Yan1(2),and Zhiming Ma1(2)
1.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
2.University of Chinese Academy of Sciences, Beijing 100049, China.
3 Hangzhou Research Center, Huawei Technologies Co., Ltd., Hangzhou 310052, Zhejiang Province, China.
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