Three Types Of Combinatorial Configurations Related To Coding Theory And Cryptography

In this thcesis.we mainly discuss three types of combinatorial configurations and their applica.tions in coding theory and cryptography.First.we use a repairable distribution packing design to construct a repairable threshold scheme which is denoted by(n.,b.k)-RTS.Xext,we use an ordered 3-design OD(3.4.n)to construct a class of constant-composition codes which is denoted by(n.3.[1.1.1.1])5-codes.At last,we discuss the existence of directed group divisible 3-design which is denoted by DGDDλ(3,4.gn＋s)s of type gn s1.This thesis consists of five chapters and it is organized as follows.In Chapter 1.we introduce the research b ackground of the full text.In C hapter 2.we give some basic concepts and related results.In Chapter 3.we construct some repairable thre)shold schemes(n.b.k)-RTSs by studying the repairable distribution designs contains a basic repairing set.and obtain the following results.(1)For any int eger r≥k(k-1)/2,with two classes of exceptions.there exists a(2.[2ν/k].k)－RTS with information rate(k-1)/k and communication complexity k//(k-1).where every share is in(Fo)k.(2)For any integer v≥6,v≠7.[2v/3]≤b≤o(v.3)or v = 7.b= 5.there exists a(2.b.3)-RTS with information rate 2/3 and communication complexity 3/2.where every share is in(FQ)3.(3)For any integer v≥10.[2v/4]≤b≤(?)(v.4),with some finite possilble exceptions,there exists a(2.b.4)-RTS with information rate 3/4 and communication complexity 4/3.where ever share is in(FQ)4.In Chapter 4.we construct a class of constant-composition codes with weight four,distziaice three and compositicion[1,1,1,1]by ordered 3-design OD(3.4,n)s.It is shown that for any integer n≥5,n ≠ 7.n=0.1,2,4.5,7.8,10(mod 12).A5(n,3,[1.1.1.1)=n(n-1)(n-2).In Chapter 5,we mainly investigate the existence of DGDDλ(3,4.gn+s)s with type gn s1 by direct and recursive constructions.For any λ≥1.we almost prove that the necessary conditions are also sufficient for n = 4.And we basically determine the existencce for n=5 with the possible exceptions λ≡ 1(mod 2).g≡ 1(mod 2),s≡ 1(mod 2),0≤s≤g.