Improved Spectral Bound for Quasi-Cyclic Codes

Luo, Gaojun
Ezerman, Martianus Frederic
Ling, San
Özkaya, Buket
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.
Citation Formats
G. Luo, M. F. Ezerman, S. Ling, and B. Özkaya, “Improved Spectral Bound for Quasi-Cyclic Codes,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 1–1, 2024, Accessed: 00, 2024. [Online]. Available: