Title :
A MacWilliams formula for Convolutional Codes
Author :
Sole, P. ; Zinoviev, D.
Author_Institution :
CNRS-I3S, Sophia Antipolis
Abstract :
Regarding convolutional codes as polynomial analogues of arithmetic lattices, we derive a Poisson Jacobi formula for their trivariate weight enumerator. The proof is based on harmonic analysis on locally compact abelian groups as developed in Tate´s thesis to derive the functional equation of the zeta function.
Keywords :
Jacobian matrices; convolutional codes; group theory; harmonic analysis; polynomial matrices; stochastic processes; Abelian groups; MacWilliams formula; Poisson Jacobi formula; Tate thesis; arithmetic lattice; convolutional codes; harmonic analysis; polynomial analogue; trivariate weight enumerator; zeta functional equation; Arithmetic; Block codes; Convolutional codes; Galois fields; Hamming weight; Harmonic analysis; Jacobian matrices; Lattices; Poisson equations; Polynomials;
Conference_Titel :
Information Theory, 2007. ISIT 2007. IEEE International Symposium on
Conference_Location :
Nice
Print_ISBN :
978-1-4244-1397-3
DOI :
10.1109/ISIT.2007.4557623
