New constructions for optical orthogonal codes, distinct difference sets and synchronous optical orthogonal codes

New Construction of DDS and DTS Next we show that the concept of an OOC with X = 1 coincides with that of Distinct Difference Sets (DDS) and that such OOCs can be used to construct Difference Triangle Sets. A ( U , k , t)-distinct difference set (DDS) of order U is a family (B,Ji E I, t = 111) of subsets of Z, each of cardinality k , such that amongst the differences ( a b)a,b E B,; a # b;i E I ) , each nonzero element g E 2, occurs at most once. An ( I , J ) difference triangle set (DTS) is a set A = {AI, A2, . . , AI},