Constant Weight Codes: An Approach Based on Knuth's Balancing Method

In this article, we study properties and algorithms for constructing sets of constant weight codewords with bipolar symbols, where the sum of the symbols is a constant q, q\neq 0. We show various code constructions that extend Knuth's balancing vector scheme, q=0, to the case where q>0. We compute the redundancy of the new coding methods. Finally, we generalize the proposed methods to encoding of imbalanced arrays in two or more dimensions.