Very Efficient Balanced Codes

The prior art construction of sets of balanced codewords by Knuth is attractive for its simplicity and absence of look-up tables, but the redundancy of the balanced codes generated by Knuth´s algorithm falls a factor of two short with respect to the minimum required. We present a new construction, which is simple, does not use look-up tables, and is less redundant than Knuth´s construction. In the new construction, the user word is modified in the same way as in Knuth´s construction, that is by inverting a segment of user symbols. The prefix that indicates which segment has been inverted, however, is encoded in a different, more efficient, way.