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...

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Main Authors: Luo, Gaojun, Ezerman, Martianus Frederic, Ling, San, Özkaya, Buket
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2024
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Online Access:https://hdl.handle.net/10356/174996
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Mathematical Sciences
Quasi-cyclic code
Minimum distance
Spectral bound
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
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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Luo, Gaojun
Ezerman, Martianus Frederic
Ling, San
Özkaya, Buket
format Article
author Luo, Gaojun
Ezerman, Martianus Frederic
Ling, San
Özkaya, Buket
author_sort Luo, Gaojun
title Improved spectral bound for quasi-cyclic codes
title_short 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_sort improved spectral bound for quasi-cyclic codes
publishDate 2024
url https://hdl.handle.net/10356/174996
_version_ 1800916358645415936