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A coding scheme of $(k+1)$ -ary error-correcting signature codes for a noisy multiple-access adder channel is proposed. Given a signature matrix $A$ and a difference matrix $D=D^{+}-D^{-}$ a priori, a larger signature matrix is obtained by replacing each element in the Hadamard matrix with $A$ , or $D^{+}$ , or $D^{-}$ depending on the values of the elements and their locations in the Hadamard...
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