The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace

被引：1
|
作者：
Cakiroglu, Yagmur [1 ]
Yayla, Oguz [2 ]
Yilmaz, Emrah Sercan [3 ]
机构：
[1] Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey
[2] Middle East Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkey
[3] Atilim Univ, Dept Math, TR-06830 Ankara, Turkey
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2022年 / 90卷 / 10期
关键词：
Irreducible polynomials; Finite fields; Trace function; Algebraic curves; CURVES; ENUMERATION; GF(2);
D O I：
10.1007/s10623-022-01088-2
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.
引用
收藏
页码：2407 / 2417
页数：11
相关论文
共 50 条
  • [1] The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace
    Yağmur Çakıroğlu
    Oğuz Yayla
    Emrah Sercan Yılmaz
    Designs, Codes and Cryptography, 2022, 90 : 2407 - 2417
  • [2] The number of irreducible polynomials over finite fields of characteristic 2 with given trace and subtrace
    Ri, Won-Ho
    Myong, Gum-Chol
    Kim, Ryul
    Rim, Chang-Il
    FINITE FIELDS AND THEIR APPLICATIONS, 2014, 29 : 118 - 131
  • [3] Irreducible polynomials over finite fields with prescribed trace/prescribed constant term
    Yucas, JL
    FINITE FIELDS AND THEIR APPLICATIONS, 2006, 12 (02) : 211 - 221
  • [4] On the parity of the number of irreducible factors of self-reciprocal polynomials over finite fields
    Ahmadi, Omran
    Vega, Gerardo
    FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (01) : 124 - 131
  • [5] Self-Reciprocal Irreducible Polynomials Over Finite Fields
    Joseph L. Yucas
    Gary L. Mullen
    Designs, Codes and Cryptography, 2004, 33 : 275 - 281
  • [6] Self-reciprocal irreducible polynomials over finite fields
    Yucas, JL
    Mullen, GL
    DESIGNS CODES AND CRYPTOGRAPHY, 2004, 33 (03) : 275 - 281
  • [7] Number of irreducible polynomials in several variables over finite fields
    Bodin, Arnaud
    AMERICAN MATHEMATICAL MONTHLY, 2008, 115 (07): : 653 - 660
  • [8] Permutation polynomials from trace functions over finite fields
    Zeng, Xiangyong
    Tian, Shizhu
    Tu, Ziran
    FINITE FIELDS AND THEIR APPLICATIONS, 2015, 35 : 36 - 51
  • [9] The number of irreducible polynomials and Lyndon words with given trace
    Ruskey, F
    Miers, CR
    Sawada, J
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2001, 14 (02) : 240 - 245
  • [10] CONSTRUCTING IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS
    Ling, San
    Ozdemir, Enver
    Xing, Chaoping
    MATHEMATICS OF COMPUTATION, 2012, 81 (279) : 1663 - 1668
12345