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- W3177643437 abstract "Abstract We analyse the behaviour of the Euclidean algorithm applied to pairs ( g , f ) of univariate nonconstant polynomials over a finite field $mathbb{F}_{q}$ of q elements when the highest degree polynomial g is fixed. Considering all the elements f of fixed degree, we establish asymptotically optimal bounds in terms of q for the number of elements f that are relatively prime with g and for the average degree of $gcd(g,f)$ . We also exhibit asymptotically optimal bounds for the average-case complexity of the Euclidean algorithm applied to pairs ( g , f ) as above." @default.
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- W3177643437 date "2021-07-06" @default.
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- W3177643437 title "Average-case complexity of the Euclidean algorithm with a fixed polynomial over a finite field" @default.
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- W3177643437 doi "https://doi.org/10.1017/s0963548321000274" @default.
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