Factorization of trinomials over galois fields of characteristic 2

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Abstract

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,xn+axk+b∈GF(2t)[x] is reducible if bothn,tare even, except possibly whenn= 2k,kodd. The caset= 1 was treated by R. G. Swan (Pacific J. Math.12,No. 2 (1962), 1099-1106), who showed thatxn+xk+ 1 is reducible overGF(2) if 8|n.

Original languageEnglish
Pages (from-to)370-377
Number of pages8
JournalFinite Fields and Their Applications
Volume3
Issue number4
DOIs
StatePublished - Oct 1997

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