TY - GEN
T1 - Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes
AU - Zeh, Alexander
AU - Wachter-Zeh, Antonia
AU - Gadouleau, Maximilien
AU - Bezzateev, Sergey
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Bound on the Minimum Distance
KW - Cyclic Code
KW - Cyclic Product Code
KW - Efficient Decoding
UR - http://www.scopus.com/inward/record.url?scp=84890322014&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2013.6620201
DO - 10.1109/ISIT.2013.6620201
M3 - Conference contribution
AN - SCOPUS:84890322014
SN - 9781479904464
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 126
EP - 130
BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013
T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013
Y2 - 7 July 2013 through 12 July 2013
ER -