A Result on Zetterberg Codes

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.