On the lifted Zetterberg code

The even-weight subcode of a binary Zetterberg code is a cyclic code with generator polynomial , where p(x) is the minimum polynomial over GF(2) of an element of order in and m is even. This even binary code has parameters . The quaternary code obtained by lifting the code to the alphabet is shown to have parameters , where denotes the minimum Lee distance. The image of the Gray map of the lifted code is a binary code with parameters , where denotes the minimum Hamming weight and . For these parameters equal the parameters of the best known binary linear code for this length and dimension. Furthermore, a simple algebraic decoding algorithm is presented for these -codes for all even m. This appears to be the first infinite family of -codes of length with having an algebraic decoding algorithm.