Chen, Weihong; Zhu, Yuefei A proof of a linear combination lemma on \(\mathbb{Z}_m\). (Chinese. English summary) Zbl 0923.11168 Appl. Math., Ser. A (Chin. Ed.) 13, No. 4, 447-450 (1998). Authors’ abstract: The paper gives a proof of a linear combination lemma on \(\mathbb{Z}_m\), i.e., the discrete random variable \(Z\) is independent of the \(k\) independent random variables \(Y_1,\dots,Y_k\) if and only if \(Z\) is independent of the sum \(c_1Y_1+\cdots +c_kY_k\) for very choice of \(c_1, \dots, c_k\), not all zero and \(\text{gcd}(\text{gcd}(c_1, \dots,c_k),m) =1\). MSC: 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 94A60 Cryptography Keywords:linear combination lemma; independent random variables PDFBibTeX XMLCite \textit{W. Chen} and \textit{Y. Zhu}, Appl. Math., Ser. A (Chin. Ed.) 13, No. 4, 447--450 (1998; Zbl 0923.11168)