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

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

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, December). Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes. Presented at 2013 IEEE International Symposium on Information Theory, Istanbul, Turkey

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 2013 IEEE International Symposium on Information Theory
• 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
• Public URL: https://durham-repository.worktribe.com/output/1156554
• Additional Information: Conference dates: 07 Jul - 12 Jul 2013