Design of some new efficient balanced codes

A balanced code with r check bits and k information bits is a binary code of length k+r and cardinality 2^k such that each codeword is balanced; that is, it has [(k+r)/2] 1´s and [(k+r)/2] 0´s. This paper contains new methods to construct efficient balanced codes. To design a balanced code, an information word with a low number of 1´s or 0´s is compressed and then balanced using the saved space. On the other hand, an information word having almost the same number of 1´s and 0´s is encoded using the single maps defined by Knuth´s (1986) complementation method. Three different constructions are presented. Balanced codes with r check bits and k information bits with k⩽2^r+1-2, k⩽3×2^r-8, and k⩽5×2^r-10r+c(r), c(r)∈{-15, -10, -5, 0, +5}, are given, improving the constructions found in the literature. In some cases, the first two constructions have a parallel coding scheme