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Factorization of Trinomials over Galois Fields of Characteristic 2

✍ Scribed by Uzi Vishne

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 200 KB
Volume: 3
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1997.0191

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✦ Synopsis

We study the parity of the number of irreducible factors of trinomials over Galois fields of characteristic 2. As a consequence, some sufficient conditions for a trinomial being reducible are obtained. For example, x n ϩ ax k ϩ b ʦ GF(2 t )[x] is reducible if both n, t are even, except possibly when n ϭ 2k, k odd. The case t ϭ 1 was treated by R. G. Swan (Pacific J. Math. 12, No. 2 (1962), 1099-1106), who showed that x n ϩ x k ϩ 1 is reducible over GF(2) if 8 ͉ n.

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