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1、广西师范大学 硕士学位论文 外差族和不相交差族的分圆构造 姓名：黄必昌 申请学位级别：硕士 专业：应用数学 指导教师：吴佃华 20070301 ? ?:?:? ?:?:?: 2004? ? ?,? ?. 2004?, Ogata, Kurosawa, Stinson?Saido 1 ? External Diff erence Families?EDF? ?. 2006? 2 ? ? Disjoint Diff erence Families?DDF? ? ?1?(v,(v 1)/2,(v 1)/2;2)-EDF. ?2?Abel?G?(v,k,k 1)-DDF. ?4?Abel?G?(v,k
2、,;u)-EDF?ku 1 are integers. Defi ne C(e) 0 = es|s = 0,1,f 1 to be the subgroup of GF(q)generated by e, and C(e) i = iC(e) 0 = es+i|s = 0,1,f 1 for each i with 0 i e 1. These C(e) i are called cyclotomic classes of order e with respect to GF(q). The cyclotomic numbers of order e, denoted (i,j)e , are
3、 defi ned as the numbers of the solution of the equation zi+ 1 = zj, zi C(e) i , zj C(e) j ,0 i,j e 1. the following results are obtained. Theorem 2.3Let q = ef+1 is an odd prime power, Dj= C(e) j1 S C(e) j2 S . S C(e) jl ?1 j h, then D = D1,D2,.,Dh is a disjoint diff erence families over GF(q) if and only if J0= J1= = Je1 where Js= h X j=1 l X t=1 l X k=1 (jt s,jk s)e,0 s e 1. Theorem 2.4 Let q = ef + 1 is an odd prime power, th
