Gauss sums, Jacobi sums, and \(p\)-ranks of cyclic difference sets

DOI10.1006/jcta.1998.2950zbMath0943.05021arXivmath/9807029OpenAlexW1975337564MaRDI QIDQ1296754

Qing Xiang, Henk D. L. Hollmann, Christian Krattenthaler, Ronald J. Evans

Publication date: 28 August 2000

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9807029

zbMATH Keywords

Gauss sumhyperovalbinary codeStickelberger's theoremGMW difference setSinger difference set

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of finite geometries (05B25) Blocking sets, ovals, (k)-arcs (51E21) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Gauss and Kloosterman sums; generalizations (11L05) Other character sums and Gauss sums (11T24) Cyclic codes (94B15) Other finite incidence structures (geometric aspects) (51E30)

Related Items

Three-valued Gauss periods, circulant weighing matrices and association schemes ⋮ Abelian difference sets of order \(n\) dividing \(\lambda\) ⋮ Character values of the Sidelnikov-Lempel-Cohn-Eastman sequences ⋮ Pure Gauss sums and skew Hadamard difference sets ⋮ Three-class association schemes from cyclotomy ⋮ Sequences with small correlation ⋮ Smith normal forms of incidence matrices ⋮ Binary cyclic codes with two primitive nonzeros ⋮ Nonlinear functions in abelian groups and relative difference sets. ⋮ Quasi-Perfect Sequences and Hadamard Difference Sets ⋮ A proof of the Welch and Niho conjectures on cross-correlations of binary \(m\)-sequences ⋮ Cameron-Liebler line classes with parameter \(x = \frac{ ( q + 1 )^2}{ 3} \) ⋮ Shift-inequivalent decimations of the Sidelnikov-Lempel-Cohn-Eastman sequences ⋮ A trace representation of binary Jacobi sequences ⋮ Recent progress in algebraic design theory ⋮ Decompositions of difference sets ⋮ The invariant factors of some cyclic difference sets

Uses Software

• gfun

Cites Work

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