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Check Character Systems Using Quasigroups: II

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Abstract

In this part of the article we continue to research check character systems with one check character over quasigroups under check equations which have one permutation. These systems always detect all single errors (i.e. errors in only one component of a code word) and can detect some other errors arising during transmission of data. We study check character systems over T-quasigroups. These quasigroups are isotopic to abelian groups and generalize the well-known class of medial quasigroups. We establish some properties of a T-quasigroup so that the check character systems over it are able to detect transpositions, jump transpositions, twin errors and jump twin errors. We also give some models of T-quasigroups, which satisfy all of the required properties for detection of errors of each of the considered types.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Academy of Sciences, Academiei str. 5, MD-2028, Chisinau, Moldova

    G. B. Belyavskaya & V. I. Izbash

  2. Mathematics Department, The Pennsylvania State University, University Park, PA, 16802, U.S.A

    G. L. Mullen

Authors
  1. G. B. Belyavskaya
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  2. V. I. Izbash
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  3. G. L. Mullen
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Corresponding author

Correspondence to G. B. Belyavskaya.

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Communicated by: P. Wild

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Belyavskaya, G.B., Izbash, V.I. & Mullen, G.L. Check Character Systems Using Quasigroups: II. Des Codes Crypt 37, 405–419 (2005). https://doi.org/10.1007/s10623-004-4033-x

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  • DOI: https://doi.org/10.1007/s10623-004-4033-x

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