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
  • [41] Irreducible compositions of polynomials over finite fields of even characteristic
    Mehrabi, Saeid
    Kyuregyan, Melsik K.
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2012, 23 (5-6) : 207 - 220
  • [42] The Trace Form Over Cyclic Number Fields
    Bolanos, Wilmar
    Mantilla-Soler, Guillermo
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2021, 73 (04): : 947 - 969
  • [43] Distribution of irreducible polynomials of small degrees over finite fields
    Ham, KH
    Mullen, GL
    MATHEMATICS OF COMPUTATION, 1998, 67 (221) : 337 - 341
  • [44] Constructions of irreducible polynomials over finite fields with even characteristic
    P. L. Sharma
    Shalini Ashima
    Mansi Gupta
    Sushil Harish
    Indian Journal of Pure and Applied Mathematics, 2023, 54 : 734 - 742
  • [45] On a Conjecture on Irreducible Polynomials over Finite Fields with Restricted Coefficients
    Ferraguti, Andrea
    Micheli, Giacomo
    ARITHMETIC OF FINITE FIELDS, WAIFI 2022, 2023, 13638 : 3 - 13
  • [46] Irreducible compositions of polynomials over finite fields of even characteristic
    Saeid Mehrabi
    Melsik K. Kyuregyan
    Applicable Algebra in Engineering, Communication and Computing, 2012, 23 : 207 - 220
  • [47] OBTAINING SPECIFIED IRREDUCIBLE POLYNOMIALS OVER FINITE-FIELDS
    GOLOMB, SW
    SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1980, 1 (04): : 411 - 418
  • [48] Distribution of irreducible polynomials of small degrees over finite fields
    Ham, K. H.
    Mullen, G. L.
    Mathematics of Computation, 67 (221):
  • [49] GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS
    Ahn, Youngwoo
    Kim, Kitae
    KOREAN JOURNAL OF MATHEMATICS, 2011, 19 (03): : 263 - 272
  • [50] Polynomial distribution and sequences of irreducible polynomials over finite fields
    Chou, WS
    Cohen, SD
    JOURNAL OF NUMBER THEORY, 1999, 75 (01) : 145 - 159
12345