Complete Weight Enumerator of Torsions and Their Applications
Let R=F2+w1F2+w2F2, where w12=w1, w22=w2, w1w2=w2w1=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 Sk,hα and Sk,hβ are given. Finally, as applications, we construct the secret sharing schemes and systematic authentication codes.
Authors
- Fanghui Ma
- Jian Gao (ORCID: https://orcid.org/0000-0003-1962-0173)
- Juan Li (ORCID: https://orcid.org/0000-0003-1509-0988)
- Daotong Qiu
Institutions
- Shandong University of Technology (CN)
- Linyi University (CN)
Publication Details
- Journal
- Mathematics
- Published
- 2025-04-01
- DOI
- https://doi.org/10.3390/math13071165
- Primary Topic
- Coding theory and cryptography
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Natural Science Foundation of Shandong Province