\(q\)-ary bent functions constructed from chain rings

DOI10.1006/ffta.1997.0200zbMath1012.05038OpenAlexW2003723729WikidataQ126653762 ScholiaQ126653762MaRDI QIDQ1267005

Xiang-Dong Hou

Publication date: 17 November 1999

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.1997.0200

zbMATH Keywords

Galois ringchain ringfinite local principal ideal ring\(q\)-ary bent functions

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Shift register sequences and sequences over finite alphabets in information and communication theory (94A55) Finite fields and commutative rings (number-theoretic aspects) (11T99) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items (13)

A new construction of perfect nonlinear functions using Galois rings ⋮ Quaternary cryptographic bent functions and their binary projection ⋮ Four decades of research on bent functions ⋮ Enumeration of isomorphism classes of extensions of \(p\)-adic fields. ⋮ Some results onq-ary bent functions ⋮ Finite commutative chain rings ⋮ Bent functions on partial spreads ⋮ Algebraic manipulation detection codes via highly nonlinear functions ⋮ Association Schemes and Directed Graphs Determined by Orbitals of General Linear Groups Over Finite Chain Rings ⋮ Generalized affine transformation monoid of a free module of finite rank over finite chain rings. ⋮ Highly nonlinear mappings ⋮ A family of partial difference sets with Denniston parameters in nonelementary abelian 2-groups ⋮ On the groups of units of finite commutative chain rings.

Cites Work

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• Generalized bent functions and their properties
• On ``bent functions
• Results on bent functions
• Relative difference sets, planar functions, and generalized Hadamard matrices
• Constructions of Partial Difference Sets and Relative Difference Sets on p -Groups
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Generalized partial spreads

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