Title :
Solving the key equation for Hermitian codes with a division algorithm
Author :
Kampf, Sabine ; Bossert, Martin ; Bouw, Irene I.
Author_Institution :
Inst. of Telecommun. & Appl. Inf. Theor., Univ. of Ulm, Ulm, Germany
fDate :
July 31 2011-Aug. 5 2011
Abstract :
This paper presents a division algorithm to solve the key equation for Hermitian codes, which is capable of locating most error patterns with weight up to half the designed minimum distance. The algorithm has a structure similar to the Euclidean algorithm used in the decoding of Reed-Solomon codes, yet it is a little more complex because bivariate polynomials have to be used. We give simulation results for the decoding of several Hermitian codes of various rates over the finite field GF(24) to verify the claims.
Keywords :
Reed-Solomon codes; computational complexity; decoding; Euclidean algorithm; Hermitian codes; Reed-Solomon codes; bivariate polynomials; decoding; division algorithm; finite field; key equation; minimum distance; Algorithm design and analysis; Complexity theory; Decoding; Mathematical model; Polynomials; Decoding of AG codes; Euclidean algorithm; Hermitian codes;
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2011.6033681
