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Hermitian codes as generalized Reed-Solomon codes

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Abstract

Hermitian codes obtained from Hermitian curves are shown to be concatenated generalized Reed-Solomon codes. This interpretation of Hermitian codes is used to investigate their structure. An efficient encoding algorithm is given for Hermitian codes. A new general decoding algorithm is given and applied to Hermitian codes to give a decoding algorithm capable of decoding up to the full error correcting capability of the code.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Tomik Yaghoobian & Ian F. Blake

Authors
  1. Tomik Yaghoobian
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  2. Ian F. Blake
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Additional information

Communicated by S. Vanstone

This work is supported by a Natural Science and Engineering Research Council Grant A7382.

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Yaghoobian, T., Blake, I.F. Hermitian codes as generalized Reed-Solomon codes. Des Codes Crypt 2, 5–17 (1992). https://doi.org/10.1007/BF00124208

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  • DOI: https://doi.org/10.1007/BF00124208

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