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

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.