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The explicit construction of irreducible polynomials over finite fields

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Abstract

For a finite field GF(q) of odd prime power order q, and n ≥ 1, we construct explicitly a sequence of monic irreducible reciprocal polynomials of degree n2m (m = 1, 2, 3, ...) over GF(q). It is the analog for fields of odd order of constructions of Wiedemann and of Meyn over GF(2). We also deduce iterated presentations of GF (q n2).

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Communicated by S.A. Vanstone

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Cohen, S.D. The explicit construction of irreducible polynomials over finite fields. Des Codes Crypt 2, 169–174 (1992). https://doi.org/10.1007/BF00124895

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  • DOI: https://doi.org/10.1007/BF00124895

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