On Weil sums, conjectures of Helleseth, and Niho exponents

DOI10.1016/j.jnt.2021.06.022zbMath1495.11138arXiv2006.15726OpenAlexW3185061983WikidataQ114156863 ScholiaQ114156863MaRDI QIDQ2071703

Liem Nguyen

Publication date: 28 January 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.15726

zbMATH Keywords

finite fieldscharacter sumsWeil sumsNiho exponentsHelleseth's vanishing conjecture

Mathematics Subject Classification ID

Exponential sums (11T23) Other character sums and Gauss sums (11T24)

Cites Work

• Unnamed Item
• New open problems related to old conjectures by Helleseth
• Weil sums of binomials, three-level cross-correlation, and a conjecture of Helleseth
• On cyclic codes of length \(2^{2^r}-1\) with two zeros whose dual codes have three weights
• Cyclic codes with few weights and Niho exponents
• On Niho type cross-correlation functions of \(m\)-sequences
• Some results about the cross-correlation function between two maximal linear sequences
• A survey on the applications of Niho exponents
• Divisibility of Weil sums of binomials
• 7. Weil sums of binomials: properties, applications and open problems
• The Geometry of m-Sequences: Three-Valued Crosscorrelations and Quadrics in Finite Projective Geometry
• Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
• Proof of a conjecture of Sarwate and Pursley regarding pairs of binary m-sequences
• On a conjecture of Helleseth regarding pairs of binary m-sequences
• Proof of a conjectured three-valued family of Weil sums of binomials
• On maximal comma-free codes (Corresp.)
• Cyclotomy of Weil sums of binomials
• A proof of the Welch and Niho conjectures on cross-correlations of binary \(m\)-sequences