On balanced codes

In a balanced code each codeword contains equally many 1's and 0's. Parallel decoding balanced codes with 2^r (or 2^r -1) information bits are presented, where r is the number of check bits. The 2²-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