A Super-Set of Patterson-Wiedemann Functions – Upper Bounds and Possible Nonlinearities

DOI10.1007/978-3-319-55227-9_16zbMath1409.94883OpenAlexW3022206788MaRDI QIDQ5267804

Ferruh Özbudak, Subhamoy Maitra, Selçuk Kavut

Publication date: 13 June 2017

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

Full work available at URL: https://doi.org/10.1007/978-3-319-55227-9_16

zbMATH Keywords

covering radiusfirst order Reed-Muller codenonlinearity boundPatterson-Wiedemann type functions

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Cryptography (94A60) Boolean functions (06E30) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75)

Cites Work

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• 9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class
• Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros
• Patterson-Wiedemann construction revisited
• Patterson–Wiedemann Type Functions on 21 Variables With Nonlinearity Greater Than Bent Concatenation Bound
• Search for Boolean Functions With Excellent Profiles in the Rotation Symmetric Class
• The covering radius of the (128,8) Reed-Muller code is 56 (Corresp.)
• On the covering radius of binary codes (Corresp.)
• On the norm and covering radius of the first-order Reed-Muller codes
• Modifications of Patterson-Wiedemann functions for cryptographic applications
• The covering radius of the<tex>(2^{15}, 16)</tex>Reed-Muller code is at least 16276
• Theory and applications of q-ary interleaved sequences
• Weight distributions of the cosets of the (32,6) Reed-Muller code

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