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Decoding of Z 2 S Linear Generalized Kerdock Codes

Author

Listed:
  • Aleksandar Minja

    (Department of Power, Electronic and Telecommunication Engineering, Faculty of Engineering (Technical Sciences), University of Novi Sad, 21000 Novi Sad, Serbia
    These authors contributed equally to this work.)

  • Vojin Šenk

    (Department of Power, Electronic and Telecommunication Engineering, Faculty of Engineering (Technical Sciences), University of Novi Sad, 21000 Novi Sad, Serbia
    These authors contributed equally to this work.
    Retired.)

Abstract

Many families of binary nonlinear codes (e.g., Kerdock, Goethals, Delsarte–Goethals, Preparata) can be very simply constructed from linear codes over the Z 4 ring (ring of integers modulo 4), by applying the Gray map to the quaternary symbols. Generalized Kerdock codes represent an extension of classical Kerdock codes to the Z 2 S ring. In this paper, we develop two novel soft-input decoders, designed to exploit the unique structure of these codes. We introduce a novel soft-input ML decoding algorithm and a soft-input soft-output MAP decoding algorithm of generalized Kerdock codes, with a complexity of O ( N S log 2 N ) , where N is the length of the Z 2 S code, that is, the number of Z 2 S symbols in a codeword. Simulations show that our novel decoders outperform the classical lifting decoder in terms of error rate by some 5 dB.

Suggested Citation

  • Aleksandar Minja & Vojin Šenk, 2024. "Decoding of Z 2 S Linear Generalized Kerdock Codes," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:443-:d:1329706
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    References listed on IDEAS

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