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- W3025790042 abstract "This paper deals with the following problem. Given a finite extension of fields $mathbb{L}/mathbb{K}$ and denoting the trace map from $mathbb{L}$ to $mathbb{K}$ by $text{Tr}$ , for which elements $z$ in $mathbb{L}$ , and $a$ , $b$ in $mathbb{K}$ , is it possible to write $z$ as a product $xy$ , where $x,yin mathbb{L}$ with $text{Tr}(x)=a,text{Tr}(y)=b$ ? We solve most of these problems for finite fields, with a complete solution when the degree of the extension is at least 5. We also have results for arbitrary fields and extensions of degrees 2, 3 or 4. We then apply our results to the study of perfect nonlinear functions, semifields, irreducible polynomials with prescribed coefficients, and a problem from finite geometry concerning the existence of certain disjoint linear sets." @default.
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- W3025790042 date "2020-05-14" @default.
- W3025790042 modified "2023-09-27" @default.
- W3025790042 title "ON THE PRODUCT OF ELEMENTS WITH PRESCRIBED TRACE" @default.
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- W3025790042 doi "https://doi.org/10.1017/s1446788720000178" @default.
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