On m-ary Balanced Codes with Parallel Decoding

An m-ary block code, m = 2, 3, 4, ..., of length n is an element of IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to left perpendicular(m - 1)n/2right perpendicular. This paper presents a tight generalization of Knuth's complementation method with parallel (hence, fast) decoding scheme. Let (n w)(m) indicate the number of m-ary words of length n and weight w is an element of {0, 1, ..., (m - 1)(n)}. A simple implementation of the scheme uses (m - 1) k + m mod 2 balancing functions to make a k is an element of IN digit information word to be balanced. So, r is an element of IN check digits can be used to balance k <= [left perpendicularr (m - 1)r/2right perpendicular)(m) - m mod 2]/(m - 1) information digits. A refined implementation of the parallel decoding scheme uses r check digits to balance k <= (m(r) - 1)/(m -1) information digits.