Hamming distance correlation for q-ary constant weight codes

Abstract

We proposed a method for q-ary constant weight codes from the cyclic difference set by generalization of the method in binary case proposed by N. Li, X. Zeng and L. Hu in 2008. It was shown that two sets of constant weight codes over Z 5 with length 21 from the (21, 5, l)-planar (cyclic) difference set and constant weight codes over G F (8) with length 57 from the (57, 8, l)-planar (cyclic) difference set have almost highest linear complexities and good profiles of their linear complexities. Moreover we investigated the value distributions in all codewords with length 57 over G F (8) from the (57, 8, l)-planar difference set. It was pointed out that this set of periodic sequences also has good value distributions and almost highest linear complexities in similar to previous set of sequences over Z 5 with period 21. In this paper we calculate the Hamming distance between all distinct cyclic shift of themselves, called the auto-Hamming correlation and the Hamming distance between distinct codewords with all cyclic shift, called the cross-Hamming correlation. Consequently it is shown that all of the auto and cross-Hamming correlations are large against their code length for all codewords over G F (8) with length 57 from a (57, 8, l)-planar difference set.