Alexander Zeh
Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes
Zeh, Alexander; Wachter-Zeh, Antonia; Gadouleau, Maximilien; Bezzateev, Sergey
Authors
Antonia Wachter-Zeh
Dr Maximilien Gadouleau m.r.gadouleau@durham.ac.uk
Associate Professor
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 | Oct 28, 2015 |
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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