Codes with a disparity property (Q679237)

In this paper the author studies a generalization of \(k^{th}\) order zero disparity codes. The zero disparity condition has been relaxed to consider a larger class of codes, \(k^{th}\) order disparity \(D\) codes. It is shown that the disparity \(D\) codes have many of the properties of zero disparity codes. The authors give an existence criterion for them and discuss the minimum distance properties. Subsets of a very specialized subclass, the first order zero disparity codes over alphabet \(A_q\) of size \(q\), are also studied. Their existence is proved when \(q\) is even and n is a multiple of \(4\), and also when \(q\) is odd and \(n\) is even.