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Let Ф(u ×v, k, Aa, Ac) be the largest possible number of codewords among all two- dimensional (u ×v, k, λa, λc) optical orthogonal codes. A 2-D (u× v, k, λa, λ)-OOC with Ф(u× v, k, λa, λc) codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D (u × v, 4, 1, 3)-OOC has been determined.