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Some three-weight linear codes and their complete weight enumerators and weight hierarchies
October 03, 2024 Β· Declared Dead Β· π Designs, Codes and Cryptography
"No code URL or promise found in abstract"
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Authors
Xiumei Li, Zongxi Chen, Fei Li
arXiv ID
2410.02209
Category
cs.IT: Information Theory
Cross-listed
math.NT
Citations
1
Venue
Designs, Codes and Cryptography
Last Checked
4 months ago
Abstract
Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic functions via a bivariate construction and then determine the complete weight enumerators and weight hierarchies of these linear codes completely. This paper generalizes some results in Li et al. (2022) and Hu et al. (2024).
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