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A General Construction of Integer Codes Correcting Specific Errors in Binary Communication Channels

Author

Listed:
  • Hristo Kostadinov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria)

  • Nikolai Manev

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl.8, 1113 Sofia, Bulgaria)

Abstract

Integer codes have been successfully applied to various areas of communication and computer technology. They demonstrate good performance in correcting specific kinds of errors. In many cases, the used integer codes are constructed by computer search. This paper presents an algebraic construction of integer codes over the ring of integers modulo A = 2 n + 1 capable of correcting at least up to two bit errors in a single b -byte. Moreover, the codes can correct some configurations of three or more erroneous bits, but not all possible ones. The construction is based on the use of cyclotomic cosets of 2 modulo A .

Suggested Citation

  • Hristo Kostadinov & Nikolai Manev, 2023. "A General Construction of Integer Codes Correcting Specific Errors in Binary Communication Channels," Mathematics, MDPI, vol. 11(11), pages 1-8, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2521-:d:1160176
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    References listed on IDEAS

    as
    1. Hristo Kostadinov & Nikolai Manev, 2021. "Integer Codes Correcting Asymmetric Errors in Nand Flash Memory," Mathematics, MDPI, vol. 9(11), pages 1-9, June.
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