Complete Weight Enumerator of Torsions and Their Applications

Daotong Qiu, Fanghui Ma (), Jian Gao and Juan Li
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Daotong Qiu: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Fanghui Ma: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Jian Gao: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
Juan Li: School of Mathematics and Statistics, Linyi University, Linyi 276000, China

Mathematics, 2025, vol. 13, issue 7, 1-22

Abstract: Let R = F 2 + w 1 F 2 + w 2 F 2 , where w 1 2 = w 1 , w 2 2 = w 2 , w 1 w 2 = w 2 w 1 = 0 . Firstly, we explore the algebraic structure of the torsion codes of MacDonald codes of types α and β over R . Secondly, the complete weight enumerator of S k , h α and S k , h β are given. Finally, as applications, we construct the secret sharing schemes and systematic authentication codes.

Keywords: torsion codes; complete weight enumerator; secret sharing schemes; authentication codes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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