A note on the relation between a sampling theorem for functions over a GF(q)n Domain and linear codes

Authors:
Yoshifumi Ukita;Tomohiko Saito;Toshiyasu Matsushima;Shigeichi Hirasawa
Affiliations:
Department of Management Information, Yokohama College of Commerce, Yokohama, Kanagawa, Japan and Cyber University, Tokyo, Japan;College of Science and Engineering, Aoyama Gakuin University, Sagamihara, Kanagawa, Japan and Cyber University, Tokyo, Japan;School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan and Cyber University, Tokyo, Japan;Research Institute for Science and Engineering, Waseda University, Tokyo, Japan and Cyber University, Tokyo, Japan
Venue:
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Year:
2009

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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.