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

Autor: Yang S; School of Mathematical Sciences, Qufu Normal University, Jining 273165, China., Zhang T; School of Mathematical Sciences, Qufu Normal University, Jining 273165, China.; School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China., Yao ZA; School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China.
Jazyk: angličtina
Zdroj: Entropy (Basel, Switzerland) [Entropy (Basel)] 2024 May 27; Vol. 26 (6). Date of Electronic Publication: 2024 May 27.
DOI: 10.3390/e26060455
Abstrakt: 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.
Databáze: MEDLINE
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