The coefficients of primitive

polynomials over finite fields

Author:
Wen Bao Han

Journal:
Math. Comp. **65** (1996), 331-340

MSC (1991):
Primary 11T06

DOI:
https://doi.org/10.1090/S0025-5718-96-00663-1

MathSciNet review:
1320895

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Abstract | References | Similar Articles | Additional Information

Abstract: For , we prove that there always exists a primitive polynomial of degree over a finite field with the first and second coefficients prescribed in advance.

**1**S. D. Cohen,*Primitive elements and polynomials with arbitrary traces*, Discrete Math. (2)**83**(1990), 1--7 MR**91h:11143**.**2**------,*Primitive elements and polynomials*, Lecture Notes in Pure and Appl. Math., vol. 141, edited by G. L. Mullen and P. J. Shiue, Marcel Dekker, New York, 1992, pp. 43--55 MR*:*existence results**93k:11113**.**3**H. Davenport,*Bases for finite fields*, J. London Math. Soc.**43**(1968), 21--39 MR**37:2729**.**4**W.-B. Han,*Primitive roots and linearized polynomials*, Adv. in Math. (China)**22**(1994), 460--462 CMP**1994:8**.**5**T. Hansen and G. L. Mullen,*Primitive polynomials over finite fields*Math. Comp.**59**(1992), 639--643 MR**93a:11101**.**6**D. Jungnickel and S. A. Vanstone,*On primitive polynomials over finite fields*, J. Algebra**124**(1989), 337--353 MR**90k:11164**.**7**R. Lidl and H. Niederreiter,*Finite fields*, Addison-Wesley, Reading, MA, 1983 MR**86c:11106**.**8**H. W. Lenstra and R. J. Schoof,*Primitive normal bases for finite fields*, Math. Comp.**48**(1987), 217--232 MR**88c:11076**.**9**O. Moreno,*On the existence of a primitive quadratic of trace*, J. Combin. Theory Ser. A*1*over**51**(1989), 104--110 MR**90b:11133**.**10**W. M. Schmidt,*Equations over finite fields*, Lecture Notes in Math., vol. 536, Springer-Verlag, Berlin and New York, 1976 MR*;*an elementary approach**55:2744**.**11**Q. Sun and W.-B. Han,*The absolute trace function and primitive roots in finite fields (in Chinese)*, Chinese Ann. Math. Ser. A**11**(1990), 202--205.**12**------,*Improvement of Weil exponential sums and its application*, preprint.

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Additional Information

**Wen Bao Han**

Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, The People’s Republic of China

DOI:
https://doi.org/10.1090/S0025-5718-96-00663-1

Keywords:
Finite field,
primitive polynomial

Received by editor(s):
January 12, 1994

Received by editor(s) in revised form:
June 2, 1994, and December 5, 1994

Article copyright:
© Copyright 1996
American Mathematical Society