Linear Codes and Self-Polarity

Linear Codes and Self-Polarity

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...

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Veröffentlicht in:Mathematics (Basel) 2024-11, Vol.12 (22), p.3555
Hauptverfasser: Bouyukliev, Iliya, Bouyuklieva, Stefka, Dzhumalieva-Stoeva, Mariya, Bikov, Dushan
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Codes
Coding theory
Fields (mathematics)
Geometry
Linear codes
Linear systems
Mathematical research
projective dual transform
projective self-dual codes
self-polar codes
symmetric matrices
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Beschreibung
Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12223555