Improved spectral bound for quasi-cyclic codes
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 boun...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2024
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| Online Access: | https://hdl.handle.net/10356/174996 |
| _version_ | 1811687389367631872 |
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| author | Luo, Gaojun Ezerman, Martianus Frederic Ling, San Özkaya, Buket |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Luo, Gaojun Ezerman, Martianus Frederic Ling, San Özkaya, Buket |
| author_sort | Luo, Gaojun |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:15:32Z |
| format | Journal Article |
| id | ntu-10356/174996 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:15:32Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1749962024-04-22T15:36:46Z Improved spectral bound for quasi-cyclic codes Luo, Gaojun Ezerman, Martianus Frederic Ling, San Özkaya, Buket School of Physical and Mathematical Sciences Division of Mathematical Sciences Mathematical Sciences Quasi-cyclic code Minimum distance Spectral bound 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. Nanyang Technological University Submitted/Accepted version The work of Gaojun Luo, Martianus Frederic Ezerman, and San Ling is supported by Nanyang Technological University Research Grant 04INS000047C230GRT01. 2024-04-18T07:33:10Z 2024-04-18T07:33:10Z 2024 Journal Article Luo, G., Ezerman, M. F., Ling, S. & Özkaya, B. (2024). Improved spectral bound for quasi-cyclic codes. IEEE Transactions On Information Theory. https://dx.doi.org/10.1109/TIT.2024.3364489 0018-9448 https://hdl.handle.net/10356/174996 10.1109/TIT.2024.3364489 en 04INS000047C230GRT01 IEEE Transactions on Information Theory © 2024 IEEE. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1109/TIT.2024.3364489. application/pdf |
| spellingShingle | Mathematical Sciences Quasi-cyclic code Minimum distance Spectral bound Luo, Gaojun Ezerman, Martianus Frederic Ling, San Özkaya, Buket Improved spectral bound for quasi-cyclic codes |
| title | Improved spectral bound for quasi-cyclic codes |
| title_full | Improved spectral bound for quasi-cyclic codes |
| title_fullStr | Improved spectral bound for quasi-cyclic codes |
| title_full_unstemmed | Improved spectral bound for quasi-cyclic codes |
| title_short | Improved spectral bound for quasi-cyclic codes |
| title_sort | improved spectral bound for quasi cyclic codes |
| topic | Mathematical Sciences Quasi-cyclic code Minimum distance Spectral bound |
| url | https://hdl.handle.net/10356/174996 |
| work_keys_str_mv | AT luogaojun improvedspectralboundforquasicycliccodes AT ezermanmartianusfrederic improvedspectralboundforquasicycliccodes AT lingsan improvedspectralboundforquasicycliccodes AT ozkayabuket improvedspectralboundforquasicycliccodes |