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Generalized construction of signature code for multiple-access adder channel

We propose a generalized construction scheme of error-correcting signature code. We form a signature matrix whose rows become the non-zero codewords of the signature code. In the coding scheme, a signature matrix is obtained from a Hadamard matrix by replacing every element by an initial signature matrix or its associated matrix depending on the element's binary value. The proposed code has longer length, higher decodability, and larger cardinality. In this coding scheme, the initial signature matrix is in a general form and can be a signature matrix of any initial signature code. Different initial matrices provide different error-correcting signature codes, including conventional codes. This general form makes it possible to obtain error-correcting signature codes with a higher sum rate than conventional codes.