Further evaluations of weil sums
WebMay 26, 2024 · Weil sums of binomials: properties, applications, and open problems. We present a survey on Weil sums in which an additive character of a finite field is applied to a binomial whose individual terms (monomials) become permutations of when regarded as functions. Then we indicate how these Weil sums are used in applications, especially … WebAug 23, 2024 · The "home school" is the school that your student currently attends or would attend based on where you reside. If you have questions regarding Special Education, …
Further evaluations of weil sums
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WebThis paper proves the characteristic $3$ case of a 1976 conjecture of Helleseth: when $p=3$ and $[F:{\mathbb F}_3]$ is a power of $2$, it is shown that $W_{F,d ... WebDec 1, 2009 · The evaluation of an exponential sum over a finite field is a very hard problem in general, and it has been achieved only in certain special cases (see e.g. [1–4,10,8,6]). A common feature for the sums for which the evaluation has been succeeded seems to be that they attain only a few distinct values.
Web[1] L. Carlitz, Evaluation of some exponential sums over a finite field, Math. Nachr. 96 (1980), 319-339. [2] R. S. Coulter, Explicit evaluations of some Weil sums ... WebThe University of Queensland's institutional repository, UQ eSpace, aims to create global visibility and accessibility of UQ’s scholarly research.
WebMay 1, 2024 · Weil sums are defined by ∑ x ∈ F q χ ( f ( x)) where f ( x) ∈ F q [ X]. In [4], [5], Coulter evaluated some Weil sums given by S u ( a, b) = ∑ x ∈ F q χ ( a x p u + 1 + b x), a ∈ F q ⁎, b ∈ F q. Lemma 3 If m v be odd, then S u ( a, 0) = G ( η) η ( a) = { ( − 1) m − 1 q η ( a), if p ≡ 1 ( mod 4), ( − 1) m − 1 ( − 1) m q η ( a), if p ≡ 3 ( mod 4). WebJan 31, 2002 · In the series of works by Coulter [6,7,8] which were based on Carlitz's proof methods [4], they explicitly evaluated the Weil sums of f (x) = ax p α +1 + L (x) over F p n with linearized...
WebA PROOF OF WEIL’S BOUND ON GENERAL CHARACTER SUMS 5 In Chapter 4, using the bound (8) jN =q j
WebSep 1, 2024 · Lemma 1 on Weil sums was given by R. S. Coulter which we will convenient to calculate the length and the weight distribution of \(\mathcal {C}_D\). Lemma 1 ... Coulter, R.S.: Further evaluations of Weil sums. Acta Arithmetica 86(3), 217–226 (1998) CrossRef MathSciNet Google Scholar Du, X., Li, X., Wan, Y.: A class of linear codes with three ... orcaflex api pythonWebReferences top [1] L. Carlitz, Evaluation of some exponential sums over a finite field, Math. Nachr. 96 (1980), 319-339. Zbl0456.12011 [2] R. S. Coulter and R. W. Matthews, Planar functions and planes of Lenz-Barlotti class II, Des. orcaflex 6d buoyWebThese are the best dim sum restaurants that offer delivery near Ashburn, VA: Yen's Cafe. Mark's Duck House. Yen's Kitchen and Sushi Bar. Dumpling Queen. Hong Kong Pearl … ips kts shopWebMay 26, 2024 · Weil sums of binomials: properties, applications, and open problems. We present a survey on Weil sums in which an additive character of a finite field is applied … orcailWebFeb 14, 2024 · Evaluation of weil sums for some polynomials and associated quadratic forms February 2024 Authors: Ruikai Chen Université de Vincennes - Paris 8 Sihem Mesnager Université de Vincennes - Paris... ips knowledgeWebplay an integral part. In [1] Carlitz obtained explicit evaluations of Weil sums with f(X) = aXp+1 +bX. His methods involved rst obtaining evaluations when b = 0 and then proceeding to the general case. This article is largely a generalisation of the methods used by Carlitz in the rst part of [1]. A further article dealing with ips knee braceWebDec 1, 2009 · Stickelberger's theorem and the Gross-Koblitz formula are used to determine the value of the binary Kloosterman sum at a modulo 64, modulo 128, and modulo 256 … ips knowledgebase