Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

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 maximallength shift-register.

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