2023/11/14 by Gaojun Luo, Martianus Frederic Ezerman, Luo, Gaojun +5
Computer Science · Medicine · #Coding theory and cryptography #Cancer Mechanisms and Therapy #Peptidase Inhibition and Analysis
paper · pdf · doi:10.48550/arxiv.2311.08156
Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the corresponding eigenspaces, we provide an improved spectral bound for quasi-cyclic codes. Numerical results verify that the improved bound outperforms the Jensen bound in almost all cases. Based on the improved bound, we propose a general construction of quasi-cyclic codes with excellent designed minimum distances. For the quasi-cyclic codes produced by this general construction, the improved spectral bound is always sharper than the Jensen bound.