On q-ary constant weight sequences from cyclic difference sets

Abstract

We proposed a method for constructing q-ary constant weight sequences from the cyclic difference sets by generalization of the method in binary case proposed by N. Li, X. Zeng and L. Hu in 2008. In this paper it is shown that a set of non-constant weight sequences over Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> with length 13 from the (13, 4, 1)-cyclic difference set and a set of constant weight sequences over Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> with length 21 from the (21, 5, 1)-cyclic difference set have almost highest linear complexities and good profiles of all sequences' linear complexities. Moreover we investigate the value distribution, the linear complexity and the correlations of a set of sequences with length 57 over GF (8) from the (57, 8, 1)-cyclic difference set. It is pointed out that this set also has good value distributions and almost highest linear complexities in similar to previous two sets over Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> with length 13 and Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> with length 21.