On Some Families of Codes Related to the Even Linear Codes Meeting the Grey–Rankin Bound

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

Mathematics, 2022, vol. 10, issue 23, 1-14

Abstract: Bounds for the parameters of codes are very important in coding theory. The Grey–Rankin bound refers to the cardinality of a self-complementary binary code. Codes meeting this bound are associated with families of two-weight codes and other combinatorial structures. We study the relations among six infinite families of binary linear codes with two and three nonzero weights that are closely connected to the self-complementary linear codes meeting the Grey–Rankin bound. We give a construction method and partial classification results for such codes. The properties of the codes in the studied families and their relations help us in constructing codes of a higher dimension from codes with a given dimension.

Keywords: linear code; residual code; two-weight code; Grey–Rankin bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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