Title :
The Gleason-Prange theorem
Author :
Blahut, Richard E.
Author_Institution :
IBM Corp., Owego, NY, USA
fDate :
9/1/1991 12:00:00 AM
Abstract :
The Gleason-Prange theorem describes a nontrivial automorphism of an extended quadratic residue code. By using the Fourier transform in an appropriate extension field, methods of digital signal processing are used to make the proof transparent and the automorphism intuitive. The theorem is proved both in a field of characteristic tow and in an arbitrary field and is stated simply as a general property of the discrete Fourier transform
Keywords :
encoding; error correction codes; Fourier transform; Gleason-Prange theorem; digital signal processing; discrete Fourier transform; extended quadratic residue code; nontrivial automorphism; Codes; Conferences; Convolution; Digital signal processing; Discrete Fourier transforms; Fast Fourier transforms; Fourier transforms; Helium; Laboratories; Signal processing algorithms;
Journal_Title :
Information Theory, IEEE Transactions on
