Some codes over R=R1R2R3 and their applications in secret sharing schemes

Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring R = R 1 R 2 R 3 . We have introduced a novel family of linear codes o...

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Bibliographic Details
Published in:Afrika mathematica Vol. 35; no. 1
Main Author: Chatouh, Karima
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024
Subjects:
Applications of Mathematics
History of Mathematical Sciences
Mathematics
Mathematics and Statistics
Mathematics Education
11T71
14G50
94B05
Torsion Codes
Association schemes
Secret sharing schemes
Simplex and MacDonald codes
11TXX
ISSN:1012-9405, 2190-7668
Online Access:Get full text
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Summary:Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring R = R 1 R 2 R 3 . We have introduced a novel family of linear codes over F p . These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. R = R 1 R 2 R 3 .
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-023-01143-8