The Ubiquity of Reed-Muller Codes

Authors:
James L. Massey
Affiliations:
-
Venue:
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2001

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Abstract

It is argued that the nearly fifty-year-old Reed-Muller codes underlie a surprisingly large number of algebraic problems in coding and cryptography. This thesis is supported by examples that include some new results such as the construction of a new class of constant-weight cyclic codes with a remarkably simple decoding algorithm and a much simplified derivation of the well-known upper bound on the linear complexity of the running key produced by a nonlinearly filtered maximal-length shift-register.