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Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes

Zeh, Alexander; Wachter-Zeh, Antonia; Gadouleau, Maximilien; Bezzateev, Sergey

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Authors

Alexander Zeh

Antonia Wachter-Zeh

Sergey Bezzateev



Abstract

Two generalizations of the Hartmann-Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. The second bound is stronger and the proof is more involved. Our technique of embedding the code into a cyclic product code can be applied to other bounds, too and therefore generalizes them.

Citation

Zeh, A., Wachter-Zeh, A., Gadouleau, M., & Bezzateev, S. (2013). Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes. In International Symposium on Information Theory Proceedings (ISIT 2013), 7-12 July 2013, Istanbul, Turkey ; proceedings (126-130). https://doi.org/10.1109/isit.2013.6620201

Conference Name 2013 IEEE International Symposium on Information Theory
Conference Location Istanbul, Turkey
Publication Date Jan 1, 2013
Deposit Date Nov 6, 2013
Publicly Available Date Mar 29, 2024
Pages 126-130
Series Title IEEE International Symposium on Information Theory
Series ISSN 2157-8095
Book Title International Symposium on Information Theory Proceedings (ISIT 2013), 7-12 July 2013, Istanbul, Turkey ; proceedings
DOI https://doi.org/10.1109/isit.2013.6620201
Keywords Bound on the minimum distance, Cyclic code, Cyclic product Code, Efficient decoding
Additional Information Conference dates: 07 Jul - 12 Jul 2013

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