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Entropy
Volume 26
Issue 6
10.3390/e26060455
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Article

Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (p − 1)/2

by
Shudi Yang
1,*,
Tonghui Zhang
1,2 and
Zheng-an Yao
3
1
School of Mathematical Sciences, Qufu Normal University, Jining 273165, China
2
School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China
3
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
*
Author to whom correspondence should be addressed.
Entropy 2024, 26(6), 455; https://doi.org/10.3390/e26060455
Submission received: 14 April 2024 / Revised: 17 May 2024 / Accepted: 23 May 2024 / Published: 27 May 2024
(This article belongs to the Section Information Theory, Probability and Statistics)
Review Reports Versions Notes

Abstract

Linear codes are the most important family of codes in cryptography and coding theory. Some codes only have a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs. By setting p≡1(mod4), we constructed an infinite family of linear codes using two distinct weakly regular unbalanced (and balanced) plateaued functions with index (p−1)/2. Their weight distributions were completely determined by applying exponential sums and Walsh transform. As a result, most of our constructed codes have a few nonzero weights and are minimal.
Keywords: linear code; weight distribution; Walsh transform; plateaued function linear code; weight distribution; Walsh transform; plateaued function

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MDPI and ACS Style

Yang, S.; Zhang, T.; Yao, Z.-a. Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (p − 1)/2. Entropy 2024, 26, 455. https://doi.org/10.3390/e26060455

AMA Style

Yang S, Zhang T, Yao Z-a. Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (p − 1)/2. Entropy. 2024; 26(6):455. https://doi.org/10.3390/e26060455

Chicago/Turabian Style

Yang, Shudi, Tonghui Zhang, and Zheng-an Yao. 2024. "Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (p − 1)/2" Entropy 26, no. 6: 455. https://doi.org/10.3390/e26060455

APA Style

Yang, S., Zhang, T., & Yao, Z.-a. (2024). Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index (p − 1)/2. Entropy, 26(6), 455. https://doi.org/10.3390/e26060455

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