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：

中国国家自然科学基金; 中国博士后科学基金;

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.

引用

页数：24

共 50 条

[21] Resolution of a Conjecture on the Covering Radius of Linear Codes
Orozco, Juan Carlos
Janwa, Heeralal
COMBINATORICS, GRAPH THEORY AND COMPUTING, SEICCGTC 2021, 2024, 448 : 413 - 425
[22] Quaternary Linear Codes and Related Binary Subfield Codes
Wu, Yansheng
Li, Chengju
Xiao, Fu
IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (05) : 3070 - 3080
[23] Linear covering codes and error-correcting codes for limited-magnitude errors
Klove, Torleiv
Schwartz, Moshe
DESIGNS CODES AND CRYPTOGRAPHY, 2014, 73 (02) : 329 - 354
[24] EAQEC codes from the LCD codes decomposition of linear codes
Li, Hui
Liu, Xiusheng
QUANTUM INFORMATION PROCESSING, 2025, 24 (02)
[25] LINEAR INEQUALITIES FOR COVERING CODES .1. PAIR COVERING INEQUALITIES
ZHEN, Z
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (03) : 573 - 582
[26] Shortened Linear Codes From APN and PN Functions
Xiang, Can
Tang, Chunming
Ding, Cunsheng
IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (06) : 3780 - 3795
[27] A construction of binary linear codes from Boolean functions
Ding, Cunsheng
DISCRETE MATHEMATICS, 2016, 339 (09) : 2288 - 2303
[28] Linear codes from vectorial Boolean power functions
Chen, Yuan
Zeng, Xiangyong
Zhang, Li
Xiao, Benchang
FINITE FIELDS AND THEIR APPLICATIONS, 2020, 67 (67)
[29] Linear covering codes and error-correcting codes for limited-magnitude errors
Torleiv Kløve
Moshe Schwartz
Designs, Codes and Cryptography, 2014, 73 : 329 - 354
[30] LINEAR INEQUALITIES FOR COVERING CODES .2. TRIPLE COVERING INEQUALITIES
ZHANG, Z
LO, CM
IEEE TRANSACTIONS ON INFORMATION THEORY, 1992, 38 (06) : 1648 - 1662

← 1 2 3 4 5 →