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Primitive Polynomials over Finite Fields of Characteristic Two

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Abstract.

Let F q be a finite field of characteristic two. We prove that for any given element a F q , there exists a primitive polynomial of degree n over F q with the m-th (0<m<n) coefficient Σ m =a when n≥7, n is odd.

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Authors and Affiliations

  1. Department of Applied Mathematics, College of Information Engineering, Information Engineering University, Zhengzhou, 450002, PRC

    Fan Shuqin & Han Wenbao

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  1. Fan Shuqin
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  2. Han Wenbao
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Correspondence to Fan Shuqin.

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Keywords: Finite field, Primitive polynomial, Galois ring, Character sums over Galois ring, The sieve method.

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Shuqin, F., Wenbao, H. Primitive Polynomials over Finite Fields of Characteristic Two. AAECC 14, 381–395 (2004). https://doi.org/10.1007/s00200-003-0140-6

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  • DOI: https://doi.org/10.1007/s00200-003-0140-6

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