The family of Zetterberg codes with parameters (2 u +1, 2 u +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 2 u +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.
['Ming-Haw Jing', 'Yaotsu Chang', 'Chong-Dao Lee', 'Jian-Hong Chen', 'Zih-Heng Chen']
A Result on Zetterberg Codes