Linear codes from planar functions and related covering codes

被引：0
作者：
Wu, Yanan [1 ]
Pan, Yanbin [1 ]
机构：
[1] Chinese Acad Sci, Key Lab Math Mechanizat, Acad Math & Syst Sci, Beijing 100190, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2025年 / 101卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Linear code; Planar function; Bent function; Weight distribution; Covering code; BENT FUNCTIONS; FINITE-FIELDS;
D O I：
10.1016/j.ffa.2024.102535
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Linear codes with few weights have wide applications in consumer electronics, data storage system and secret sharing. In this paper, by virtue of planar functions, several infinite families of l-weight linear codes over F p are constructed, where l can be any positive integer and p is a prime number. The weight distributions of these codes are determined completely by utilizing certain approach on exponential sums. Experiments show that some (almost) optimal codes in small dimensions can be produced from our results. Moreover, the related covering codes are also investigated. (c) 2024 Published by Elsevier Inc.
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页数：24
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