List decoding of the first-order binary Reed-Muller codes

DOI10.1134/S0032946007030052zbMath1136.94318OpenAlexW2136695309MaRDI QIDQ927477

I. I. Dumer, Grigory Kabatiansky, Cédric Tavernier

Publication date: 9 June 2008

Published in: Problems of Information Transmission (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0032946007030052

Mathematics Subject Classification ID

Cryptography (94A60) Cyclic codes (94B15)

Related Items (11)

On the lower bounds of the second order nonlinearities of some Boolean functions ⋮ Third-order nonlinearities of a subclass of Kasami functions ⋮ On higher order nonlinearities of Boolean functions ⋮ The lower bounds on the second-order nonlinearity of three classes of Boolean functions ⋮ A lower bound on the third-order nonlinearity of the simplest \(\mathcal{PS}_{a p}\) bent functions ⋮ The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity ⋮ Higher-order nonlinearity of Kasami functions ⋮ On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations ⋮ The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity ⋮ An improved list decoding algorithm for the second order Reed-Muller codes and its applications ⋮ On the higher-order nonlinearity of a Boolean bent function class (constructed via Niho power functions)

Cites Work

• Fast decoding algorithm for first-order Reed-Muller codes
• Learning Polynomials with Queries: The Highly Noisy Case
• List Decoding of<tex>$q$</tex>-ary Reed–Muller Codes
• Unnamed Item

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