A New Bound on the Minimum Distance of Cyclic Codes Using Small-Minimum-Distance Cyclic Codes

Autor:	Zeh, Alexander, Bezzateev, Sergey
Rok vydání:	2012
Předmět:	Computer Science - Information Theory
Druh dokumentu:	Working Paper
Popis:	A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann--Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several families of cyclic codes. We define syndromes and formulate a Key Equation that allows an efficient decoding up to our bound with the Extended Euclidean Algorithm. It turns out that lowest-code-rate cyclic codes with small minimum distances are useful for our approach. Therefore, we give a sufficient condition for binary cyclic codes of arbitrary length to have minimum distance two or three and lowest code-rate Comment: Designs, Codes and Cryptography (2012)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1206.4976 Zobrazit plný text záznamu View this record from Arxiv