A Generalization of Hamming Codes

  • N. Pedroza UFRJ
  • P. E. D. Pinto UERJ
  • J. L. Szwarcfiter UFRJ / UERJ
DOI: https://doi.org/10.5753/etc.2017.3186

Abstract


We present a recursive construction of optimal linear codes of lenght n ≥ 3 and Hamming distance 3, as well as the coding and decoding processes with efficient performance. In particular, when n has the form 2r − 1 we have exactly the binary Hamming codes.

References

Hamming, R. W. (1950). Error detecting and error correcting codes. Bell System technical journal, 29(2):147–160.

Hartnett, W. E. (2012). Foundations of coding theory, volume 1. Springer Science & Business Media.

MacWilliams, F. J. and Sloane, N. J. A. (1977). The theory of error correcting codes. Elsevier.
Published
2017-07-02
How to Cite

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PEDROZA, N.; PINTO, P. E. D.; SZWARCFITER, J. L.. A Generalization of Hamming Codes. In: PROCEEDINGS OF THE THEORY OF COMPUTATION MEETING (ETC), 2. , 2017, São Paulo. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2017 . p. 37-40. ISSN 2595-6116. DOI: https://doi.org/10.5753/etc.2017.3186.