On the Covering Radii of Binary Reed–Muller Codes in the Set of Resilient Boolean Functions

DOI10.1109/TIT.2004.842779zbMath1309.94194OpenAlexW2170147734WikidataQ62045624 ScholiaQ62045624MaRDI QIDQ3547829

Bart Preneel, An Braeken, Svetla Nikova, Yuri L. Borissov

Publication date: 21 December 2008

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tit.2004.842779

Mathematics Subject Classification ID

Cryptography (94A60) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75) Boolean functions (94D10)

Related Items (8)

Boolean functions: degree and support ⋮ A construction of bent functions of \(n+2\) variables from a bent function of \(n\) variables and its cyclic shifts ⋮ On the covering radius of the third order Reed-Muller code \(\mathrm{RM}(3, 7)\) ⋮ On the construction of new bent functions from the max-weight and min-weight functions of old bent functions ⋮ New bounds on the covering radius of the second order Reed-Muller code of length 128 ⋮ Construction of bent functions of 2kvariables from a basis of ⋮ Hadamard matrices, \(d\)-linearly independent sets and correlation-immune Boolean functions with minimum Hamming weights ⋮ The covering radius of the Reed-Muller code \(\text{RM}(2, 7)\) is \(40\)

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