The necessary and sufficient condition for constructing a spreading set with decodability is investigated. It is proved that for a given delta-decodable spreading set and a qtimesq square matrix H with components 1 or -1, a qdelta-decodable spreading set S *  is obtained if and only if H is a Hadamard matrix. In addition, a decoding rule with error correction and message data detection is provided
['Jun Cheng', 'Takashi Ohira', 'Koichi Kamoi', 'Yoichiro Watanabe']
Spreading Set With Error Correction for Multiple-Access Adder Channel