DocumentCode :
925443
Title :
Convolutions over residue classes of quadratic integers
Author :
Reed, Irving S. ; Truong, T.K.
Volume :
22
Issue :
4
fYear :
1976
fDate :
7/1/1976 12:00:00 AM
Firstpage :
468
Lastpage :
475
Abstract :
A Fourier-like transform is defined over a ring of quadratic integers modulo a prime number 
in the quadratic field 
, where 
is a square-free integer. If is a Fermat prime, one can utilize the fast Fourier transform (FFT) algorithm over the resulting finite fields to yield fast convolutions of quadratic integer sequences in . The theory is also extended to a direct sum of such finite fields. From these results, it is shown that Fourier-like transforms can also be defined over the quadratic integers in 
modulo a nonprime Fermat number.
in the quadratic field , where is a square-free integer. If is a Fermat prime, one can utilize the fast Fourier transform (FFT) algorithm over the resulting finite fields to yield fast convolutions of quadratic integer sequences in . The theory is also extended to a direct sum of such finite fields. From these results, it is shown that Fourier-like transforms can also be defined over the quadratic integers in modulo a nonprime Fermat number.Keywords :
Convolution; Number-theoretic transforms; Block codes; Convolutional codes; Discrete Fourier transforms; Discrete transforms; Electrons; Error correction codes; Fast Fourier transforms; Fourier transforms; Galois fields; Welding;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1976.1055583
Filename :
1055583
Link To Document :
