arXiv subjects
Publications and source records attributed to Theo G. Swart.
We present an encoding and decoding scheme for constant weight sequences, that is, given an information sequence, the construction results in a sequence of specific weight within a certain range. The scheme uses a prefix design that is based on Gray codes. Furthermore, by adding redundant symbols we extend the range of weight values for output sequences, which is useful for some applications.
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on a generalization of Knuth's parallel balancing approach, which can handle very long information sequences. However, the overall sequence composed of the information sequence, together with the prefix must be balanced. This is reminiscent of Knuth's serial algorithm. The encoding of our construction does not make use of lookup tables, while the decoding process is simple and can be done in parallel.
We examine and compare several different classes of "balanced" block codes over q-ary alphabets, namely symbol-balanced (SB) codes, charge-balanced (CB) codes, and polarity-balanced (PB) codes. Known results on the maximum size and asymptotic minimal redundancy of SB and CB codes are reviewed. We then determine the maximum size and asymptotic minimal redundancy of PB codes and of codes which are both CB and PB. We also propose efficient Knuth-like encoders and decoders for all these types of balanced codes.