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Primitive Polynomials over Small Fields

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

Given a positive integer n, any root of a primitive polynomial x n + a 1 x n − 1 + ... + a n over the finite field \(\mathbb{F}_q\) of q elements (where q is a power of a prime p) is a primitive (generating) element of the extension \(\mathbb{F}_{q^n}\), by definition having multiplicative order q n – 1.

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© 2004 Springer-Verlag Berlin Heidelberg

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Cohen, S.D. (2004). Primitive Polynomials over Small Fields. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_16

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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