Generalized Bent Functions and Their Gray Images

DOI10.1007/978-3-319-55227-9_12zbMath1409.11135arXiv1511.01438OpenAlexW2225043332MaRDI QIDQ5267800

Thor Martinsen, Pantelimon Stănică, Wilfried Meidl

Publication date: 13 June 2017

Published in: Arithmetic of Finite Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.01438

zbMATH Keywords

Walsh spectrumgeneralized bent functionsgeneralized semibent functions

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Polynomials over finite fields (11T06) Fuzzy sets and logic (in connection with information, communication, or circuits theory) (94D05)

Related Items (13)

A survey on \(p\)-ary and generalized bent functions ⋮ Partial spread and vectorial generalized bent functions ⋮ Generalized bent functions into \(\mathbb{Z}_{p^k}\) from the partial spread and the Maiorana-McFarland class ⋮ Multiple characters transforms and generalized Boolean functions ⋮ Generalized bent Boolean functions and strongly regular Cayley graphs ⋮ Construction methods for generalized bent functions ⋮ On generalized hyper-bent functions ⋮ Bent and \(\mathbb{Z}_{2^k}\)-bent functions from spread-like partitions ⋮ Gowers \(U_2\) norm as a measure of nonlinearity for Boolean functions and their generalizations ⋮ Connections between quaternary and Boolean bent functions ⋮ \(C\)-differential bent functions and perfect nonlinearity ⋮ New Constructions of Codebooks Nearly Meeting the Welch Bound ⋮ Generalized Bent Functions and Their Gray Images

Cites Work

• Bent and generalized bent Boolean functions
• Nonexistence of generalized bent functions from \(\mathbb{Z}_{2}^{n}\) to \(\mathbb{Z}_{m}\)
• Generalized bent functions -- some general construction methods and related necessary and sufficient conditions
• Strongly regular graphs associated with ternary bent functions
• Generalized bent functions and their properties
• Partial spread and vectorial generalized bent functions
• Z/sub 2/k-linear codes
• Quaternary Constant-Amplitude Codes for Multicode CDMA
• Generalized Bent Functions and Their Gray Images

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