Some Results on Self-Complementary Linear Codes

Maria Pashinska-Gadzheva, Iliya Bouyukliev () and Valentin Bakoev
Additional contact information
Maria Pashinska-Gadzheva: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 5000 Veliko Tarnovo, Bulgaria
Iliya Bouyukliev: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 5000 Veliko Tarnovo, Bulgaria
Valentin Bakoev: Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5000 Veliko Tarnovo, Bulgaria

Mathematics, 2023, vol. 11, issue 24, 1-11

Abstract: Binary codes have a special place in coding theory since they are one of the most commonly used in practice. There are classes of codes specific only to the binary case. One such class is self-complementary codes. Self-complementary linear codes are binary codes that, together with any vector, contain its complement as well. This paper is about binary linear self-complementary codes. A natural goal in coding theory is to find a linear code with a given length n and dimension k such that the minimum distance d is maximal. Codes with these properties are called optimal. Another important issue is classifying the optimal codes, i.e., finding exactly one representative of each equivalence class. In some sense, the classification problem is more general than the minimum distance bounds problem. In this work, we summarize the classification results for self-complementary codes with the maximum possible minimum distance and a length of up to 20. For the classification, we developed a new algorithm that is much more efficient compared to existing ones in some cases.

Keywords: binary self-complementary codes; optimal codes; classification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/24/4950/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/24/4950/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:24:p:4950-:d:1299873

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().