Very Efficient Balanced Codes

@article{SchouhamerImmink2010VeryEB,
  title={Very Efficient Balanced Codes},
  author={Kees A. Schouhamer Immink and Jos H. Weber},
  journal={IEEE Journal on Selected Areas in Communications},
  year={2010},
  volume={28},
  url={https://api.semanticscholar.org/CorpusID:8596702}
}
A new construction of sets of balanced codewords is presented, which is simple, does not use look-up tables, and is less redundant than Knuth's construction.
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Methods Citations
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12 References

Knuth’s balancing of codewords revisited

This paper presents results of attempts to improve the performance of Knuthpsilas balanced codes, a very simple algorithm for constructing sets of bipolar codewords with equal numbers of dasia1psil as and dasia-1psils, called balanced codes.

On balanced codes

The 2/sup 2/-r-1 construction given by D.E. Knuth is improved and the new codes are shown to be optimal when Knuth's complementation method is used.

An Abstract of the Thesis of Title: Design of Some New Efficient Balanced Codes Design of Some New Efficient Balanced Codes Redacted for Privacy

New methods to construct efficient balanced codes based on the concept of tail-map are presented, improving the constructions found in the literature.

Design of some new Balanced Codes

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Codes for Mass Data Storage Systems (Second Edition) (K. H. Schouhamer Immink; 2004) [Book review]

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Efficient balanced codes

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