New primitive <IMG ALIGN=BOTTOM HEIGHT=32 WIDTH=55> whose degree is a Mersenne exponent期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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New primitive whose degree is a Mersenne exponent

Authors:	Toshihiro Kumada Hannes Leeb Yoshiharu Kurita Makoto Matsumoto

Institution:	Department of Mathematics, Keio University, Yokohama, Japan ; Department of Statistics, OR and Computer Methods, University of Vienna, Austria ; Hungarian Productivity Center, Budapest, Hungary ; Department of Mathematics, Keio University, Yokohama, Japan

Abstract:	All primitive trinomials over with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are $X^{859433}+X^{288477}+1$ and its reciprocal. Also two examples of primitive pentanomials over with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

Keywords:	Irreducible polynomials primitive polynomials finite field Mersenne exponent

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