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.
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页码：2407 / 2417
页数：11
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