Title :
A note on the relation between a sampling theorem for functions over a GF(q)n domain and linear codes
Author :
Ukita, Yoshifumi ; Saito, Tomohiko ; Matsushima, Toshiyasu ; Hirasawa, Shigeichi
Author_Institution :
Dept. of Manage. Inf., Yokohama Coll. of Commerce, Yokohama, Japan
Abstract :
In this paper, we generalize the sampling theorem for bandlimited functions over the Boolean domain to a sampling theorem for bandlimited functions over a GF(q)n domain. We also present a theorem for the relation between the parity check matrix of a linear code and any distinct error vectors. Lastly, we clarify the relation between the sampling theorem for functions over a GF (q)n domain and linear codes.
Keywords :
bandlimited signals; linear codes; matrix algebra; parity check codes; signal sampling; Boolean domain; bandlimited function; distinct error vectors; linear codes; parity check matrix; sampling theorem; Boolean functions; Cybernetics; Design for experiments; Educational institutions; Frequency; Linear code; Parity check codes; Sampling methods; Signal sampling; Vectors; discrete Fourier transform; error-correcting codes; experimental designs; orthogonal designs;
Conference_Titel :
Systems, Man and Cybernetics, 2009. SMC 2009. IEEE International Conference on
Conference_Location :
San Antonio, TX
Print_ISBN :
978-1-4244-2793-2
Electronic_ISBN :
1062-922X
DOI :
10.1109/ICSMC.2009.5346131
