Article

A Result on Zetterberg Codes

Dept. of Inf. Eng., I-Shou Univ., Kaohsiung, Taiwan
IEEE Communications Letters (impact factor: 0.98). 08/2010; DOI:10.1109/LCOMM.2010.07.100784 pp.662 - 663
Source: IEEE Xplore

ABSTRACT The family of Zetterberg codes with parameters (2u+1, 2u+1-2u) for even u is one of the best known double error correcting codes because of their large code rate and high decoding speed. In this letter, we prove that when u is odd, Zetterberg codes can correct all errors of weight at most two with only 2u+1 exceptions. Moreover, by multiplying (x-1) to the generator polynomials of Zetterberg codes with u odd, the cyclic codes generated are two-error correctable. A decoding algorithm is developed for the new family of Zetterberg codes.

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Keywords

cyclic codes
 
decoding algorithm
 
decoding speed
 
known double error correcting codes
 
large code rate
 
multiplying
 
u odd
 
Zetterberg codes
 

Ming-Haw Jing