On balanced codes

Abstract

In a balanced code each codeword contains equally many 1's and 0's. Parallel decoding balanced codes with 2/sup r/ (or 2/sup r/-1) information bits are presented, where r is the number of check bits. The 2/sup 2/-r-1 construction given by D.E. Knuth (ibid., vol.32, no.1, p.51-3, 1986) is improved. The new codes are shown to be optimal when Knuth's complementation method is used.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>