FIVE-LEE-WEIGHT LINEAR CODES OVER F q + u F q

被引：0

作者：

Kumar, Payan ^{[1
,2
]}

Khan, Noor mohammad ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, India

[2] Indian Inst Sci, Dept Elect Syst Engn, Bengaluru 560012, India

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2025年

关键词：

Linear code; Gauss sum; Weight distribution; Complete weight enu- merator; Secret sharing scheme; COMPLETE WEIGHT ENUMERATORS; 3-WEIGHT CODES; CONSTRUCTION;

D O I：

10.3934/amc.2025002

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this study, linear codes having their Lee-weight distributions over the semi-local ring F q + uF q with u 2 = 1 are constructed using the defining set and Gauss sums for an odd prime q. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes.

引用

页数：16

共 50 条

[41] A new extension theorem for 3-weight modulo q linear codes over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{F}_q}$$\end{document}
E. J. Cheon
T. Maruta
Designs, Codes and Cryptography, 2009, 52 (2) : 171 - 183
[42] An improved method for determining the weight distribution of a family of q-ary cyclic codes
Gerardo Vega
Applicable Algebra in Engineering, Communication and Computing, 2017, 28 : 527 - 533
[43] An improved method for determining the weight distribution of a family of q-ary cyclic codes
Vega, Gerardo
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2017, 28 (06) : 527 - 533
[44] Narrow-Sense BCH Codes Over GF(q) With Length n = qm-1/q-1
Li, Shuxing
Ding, Cunsheng
Xiong, Maosheng
Ge, Gennian
IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (11) : 7219 - 7236
[45] Complete classification of (δ plus αu2)-constacyclic codes over F3m[u]/⟨u4⟩ of length 3n
Cao, Yuan
Cao, Yonglin
Dong, Li
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2018, 29 (01) : 13 - 39
[46] Linear codes over F2 + uF2 + vF2 + uvF2
Yildiz, Bahattin
Karadeniz, Suat
DESIGNS CODES AND CRYPTOGRAPHY, 2010, 54 (01) : 61 - 81
[47] THE NUMBER OF F q-POINTS ON DIAGONAL HYPERSURFACES WITH MONOMIAL DEFORMATION
Mccarthy, Dermot
PACIFIC JOURNAL OF MATHEMATICS, 2024, 328 (02) : 339 - 359
[48] Quantum codes from cyclic codes over F3 + vF3
Ashraf, Mohammad
Mohammad, Ghulam
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2014, 12 (06)
[49] Macwilliams Identities of Linear Codes over the Ring F2+ uF2+ vF2
LIU Xiusheng
LIU Hualu
JournalofSystemsScience&Complexity, 2015, 28 (03) : 691 - 701
[50] Macwilliams identities of linear codes over the ring F2 + uF2 + vF2
Xiusheng Liu
Hualu Liu
Journal of Systems Science and Complexity, 2015, 28 : 691 - 701

← 1 2 3 4 5 →