Further results on permutation polynomials via linear translators

被引：0

作者：

Qin, Xiaoer ^{[1
]}

Yan, Li ^{[2
]}

机构：

[1] Yangtze Normal Univ, Coll Math & Stat, Chongqing 408100, Peoples R China

[2] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 09期

基金：

美国国家科学基金会;

关键词：

Permutation polynomial; linear translator; the system of linear equations; rank; FINITE-FIELDS; TRINOMIALS;

D O I：

10.1142/S0219498820501662

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by using linear translators, we characterize a new class of permutation polynomials of the form x + Sigma(k)(i=1)gamma(i)h(i)(fi(x)), which has a more general form than x +gamma h(f(x)). Then, we present the compositional inverses of such permutation polyno- mials. Furthermore, by specifying the functions h(i)(x) and f(i)(x), we can get some new permutation polynomials of the forms x + gamma(1)(Tr(beta(1)x)+delta(1))(s1) + gamma(2) (Tr(beta(2)x) + delta(2))(s2) and x+gamma(1)(Tr(x)+delta)(s)(1)+gamma(2)(Tr(x)+delta(2))(s2), where Tr(x) is the trace function.

引用

页数：18

共 50 条

[31] Some new results on permutation polynomials over finite fields
Jingxue Ma
Tao Zhang
Tao Feng
Gennian Ge
Designs, Codes and Cryptography, 2017, 83 : 425 - 443
[32] Permutation group theory and permutation polynomials
Cohen, SD
ALGEBRAS AND COMBINATORICS, 1999, : 133 - 146
[33] Further asymptotic size Ramsey results obtained via linear programming
Pikhurko, O
DISCRETE MATHEMATICS, 2003, 273 (1-3) : 193 - 202
[34] Further results on structural assignment of linear systems via sensor selection
Liu, Xinmin
Lin, Zongli
Chen, Ben A.
AUTOMATICA, 2007, 43 (09) : 1631 - 1639
[35] The zeros of random polynomials: Further results and applications
Schober, R
Gerstacker, WH
IEEE TRANSACTIONS ON COMMUNICATIONS, 2002, 50 (06) : 892 - 896
[36] FURTHER RESULTS ON THE QUALITATIVE THEORY OF GENERALIZED POLYNOMIALS
MAROULAS, J
BARNETT, S
JOURNAL OF THE INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS, 1979, 23 (01): : 33 - 42
[37] FURTHER RESULTS ON FRACTIONAL CALCULUS OF SRIVASTAVA POLYNOMIALS
Agarwal, Praveen
Jain, Shilpi
BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 3 (02): : 167 - 174
[38] Further Results on Jury Test for Complex Polynomials
Choo, Younseok
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2010, E93A (10) : 1824 - 1826
[39] Grothendieck polynomials via permutation patterns and chains in the Bruhat order
Lenart, Cristian
Robinson, Shawn
Sottile, Frank
AMERICAN JOURNAL OF MATHEMATICS, 2006, 128 (04) : 805 - 848
[40] Further results on permutation polynomials of the form (xpm - x plus δ)s + L(x) over Fp2m
Xu, Guangkui
Cao, Xiwang
Xu, Shanding
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2016, 15 (05)

← 1 2 3 4 5 →