AVERAGE DISTANCE AND MINIMUM AVERAGE DISTANCE OF BINARY CONSTANT WEIGHT CODE AND ITS PROPERTIES

Abstract

Let [Formula: see text] denote the average Hamming distance of a binary constant weight code C. Ai is the distance distribution of C and Bj is the transform quantity of Ai. Let β(n, M, w) denote the minimum average Hamming distance of a binary constant weight code with length n, size M, and weight w. In this paper, we have established the relation among Bj, [Formula: see text] and Ai. We also study the problem of determining β(n, M, w) and bounds of β(n, M, w) for different values of M.