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Boolean Functions; Extended Cyclic Code; Information Theory; Symmetric Cryptography
Definition
The Reed–Muller code of length 2m and order r is the linear binary code whose codewords can be identified to Boolean functions of m variables and of algebraic degree less than or equal to r.
Background
Coding theory
Theory
It is well known that any property of Reed–Muller codes is a property of Boolean functions. Reed–Muller codes provide a natural way to quantify the degree, the nonlinearity, the correlation-immunity, or the propagation criterion of a Boolean function [1]. On the other hand, Reed–Muller codes are an important class of error-correcting codes, in particular they can be viewed as extended cyclic codes. They play a crucial role in the study of important families of cryptographic mappings, such as permutations on finite fields. Here, the multivariable definition of Reed–Muller codes is presented. More on Reed–Muller codes can be found...
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Massey JL (1995) Some applications of coding theory in cryptography. In: Farell PG (ed) Codes and ciphers: cryptography and coding IV. Formara, Essex, pp 33–47
Pless VS, Huffman WC, Brualdi RA (1998) An introduction to algebraic codes. Handbook of coding theory, part 1: algebraic coding, chapter 1. Elsevier, Amsterdam
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Charpin, P. (2011). Reed–Muller Codes. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_366
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_366
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5905-8
Online ISBN: 978-1-4419-5906-5
eBook Packages: Computer ScienceReference Module Computer Science and Engineering