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Let v=p1m1p2m2…ptmt be the canonical prime factorization of v. In this paper, we give a construction of optimal ((s+1)×v,s+1,1) two-dimensional optical orthogonal codes with both at most one-pulse per wavelength and at most one-pulse per time slot, where s | gcd(p1-1,p2-1,...,pt-1). The method is much simpler than that in [1]. Optimal (m×v,k,1) two-dimensional optical orthogonal codes are also constructed based on the Steiner system S[2,k,m].
Tomoharu SHIBUYA Masatoshi ONIKUBO Kohichi SAKANIWA
In this paper, we investigate Tanner's lower bound for the minimum distance of regular LDPC codes based on combinatorial designs. We first determine Tanner's lower bound for LDPC codes which are defined by modifying bipartite graphs obtained from combinatorial designs known as Steiner systems. Then we show that Tanner's lower bound agrees with or exceeds conventional lower bounds including the BCH bound, and gives the true minimum distance for some EG-LDPC codes.