A NOTE ON THE KERNEL OF TRACE OVER FINITE FIELDS

被引：0

作者：

Jin, Yong ^{[1
]}

Jiang, Jing-jing ^{[1
]}

Shen, Lin-zhi ^{[1
]}

机构：

[1] Civil Aviat Univ China, Coll Sci, Tianjin, Peoples R China

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2023年 / 24卷 / 02期

关键词：

Finite field; linear code; kinearized polynomial; trace; LINEARIZED POLYNOMIALS; HAMMING WEIGHTS; CODES; NUMBER; ROOTS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

To decide dim(ker(L) n ker(Tr)) from the perspective of the coeffi-cients of a linearized polynomial L, we turn the problem into considering about the kernel of another linearized polynomial L-1. In a more algebraic way, we solve this problem in the case the coefficients of L belong to the prime subfield, and classes of linearized polynomials Ls can be given such that dim(ker(L) n ker(Tr)) = s for a given s.

引用

页码：251 / 259

页数：9

共 50 条

[41] A NOTE ON THE EXISTENCE OF NON-SIMPLE DESIGNS OVER FINITE FIELDS
Braun, Michael
INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2012, 5 (01): : 85 - 89
[42] A NOTE ON THE CLASSICAL LINEAR-GROUPS OVER FINITE-FIELDS
HARRIS, ME
REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 1982, 27 (02): : 159 - 167
[43] Trace of products in finite fields
Swaenepoel, Cathy
FINITE FIELDS AND THEIR APPLICATIONS, 2018, 51 : 93 - 129
[44] A note on divisor class groups of degree zero of algebraic function fields over finite fields
Özbudak, F
FINITE FIELDS AND THEIR APPLICATIONS, 2003, 9 (01) : 129 - 133
[45] Existence of primitive normal pairs with one prescribed trace over finite fields
Hariom Sharma
R. K. Sharma
Designs, Codes and Cryptography, 2021, 89 : 2841 - 2855
[46] Existence of primitive normal pairs with one prescribed trace over finite fields
Sharma, Hariom
Sharma, R. K.
DESIGNS CODES AND CRYPTOGRAPHY, 2021, 89 (12) : 2841 - 2855
[47] Irreducible polynomials over finite fields with prescribed trace/prescribed constant term
Yucas, JL
FINITE FIELDS AND THEIR APPLICATIONS, 2006, 12 (02) : 211 - 221
[48] A note on powers in finite fields
Aabrandt, Andreas
Hansen, Vagn Lundsgaard
INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, 2016, 47 (06) : 987 - 991
[49] Deciding finiteness for matrix semigroups over function fields over finite fields - A note on a paper by Rockmore, Tan, and Beals
Ivanyos, G
ISRAEL JOURNAL OF MATHEMATICS, 2001, 124 (1) : 185 - 188
[50] A Note on Security of Knapsack PKC Using Plaintext Encoding Over Finite Fields
Nasako, Takeshi
Murakami, Yasuyuki
2008 INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY AND ITS APPLICATIONS, VOLS 1-3, 2008, : 1207 - 1212

← 1 2 3 4 5 →