Check character systems using quasigroups: II

G. B. Belyavskaya, V. I. Izbash, G. L. Mullen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)405-419
Number of pages15
JournalDesigns, Codes, and Cryptography
Issue number3
StatePublished - Dec 2005

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Applied Mathematics


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