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Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q~n) such that α + α~(-1)is also primitive or α + α~(-1)is primitive and α is a normal element of F_(q~n) over F_q. 相似文献
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Primitive normal polynomials with a prescribed coefficient 总被引:1,自引:0,他引:1
In this paper, we established the existence of a primitive normal polynomial over any finite field with any specified coefficient arbitrarily prescribed. Let n15 be a positive integer and q a prime power. We prove that for any aFq and any 1m<n, there exists a primitive normal polynomial f(x)=xn−σ1xn−1++(−1)n−1σn−1x+(−1)nσn such that σm=a, with the only exceptions σ1≠0. The theory can be extended to polynomials of smaller degree too. 相似文献
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