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A property of polynomials over a finite field

Published online by Cambridge University Press:  26 February 2010

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Extract

Let q be a power of an odd prime, [q] denote the Galois field GF(q) and write X(x) = xq − x. Let f(x) be a polynomial, having no linear factors, over [q], of positive degree, and write . Consider the continued fraction expansions

and

where the Ai(x) and aj,(x) are polynomials over [q] of degree ≥ 1 (if i ≥ 1, j ≥ 1). Plainly A0(x) = ao(x). Suppose that n = nf is the integer denned uniquely as the largest m such that

Type
Research Article
Copyright
Copyright © University College London 1975

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