Linear Codes and Self-Polarity

Iliya Bouyukliev (), Stefka Bouyuklieva, Mariya Dzhumalieva-Stoeva and Dushan Bikov
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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

Mathematics, 2024, vol. 12, issue 22, 1-18

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.

Keywords: linear codes; projective dual transform; projective self-dual codes; self-polar codes; symmetric matrices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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