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Linear Codes and Self-Polarity

Author

Listed:
  • Iliya Bouyukliev

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

  • Stefka Bouyuklieva

    (Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5003 Veliko Tarnovo, Bulgaria)

  • Mariya Dzhumalieva-Stoeva

    (Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5003 Veliko Tarnovo, Bulgaria)

  • Dushan Bikov

    (Faculty of Computer Science, Goce Delcev University, 2000 Stip, North Macedonia)

Abstract

This work studies projective self-dual (PSD) and self-polar linear codes over finite fields with q elements, where q is a power of a prime. The possible parameters for which PSD codes may exist are presented, and many examples are provided. Algorithms for checking whether a q -ary linear code is self-polar are described. Many PSD and self-polar codes over fields with two, three, four, and five elements with two and three nonzero weights are constructed.

Suggested Citation

  • Iliya Bouyukliev & Stefka Bouyuklieva & Mariya Dzhumalieva-Stoeva & Dushan Bikov, 2024. "Linear Codes and Self-Polarity," Mathematics, MDPI, vol. 12(22), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3555-:d:1520828
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