Strong Multimedia Identifiable Parent Property Codes And Their Relevance Research

In order to reduce the codeword length,Cheng and Jiang et al.proposed concepts of multimedia identifiable parent property code(MIPPC in short)and strong multimedia identifiable parent property code(SMIPPC in short)which also have traceability.However there arc little results on MIPPC and SMIPPC since their structures are too complexity.So it is important to study the two types fingerprinting codes.The following notations are useful for introduce definitions of MIPPC and SMIPPC.Let n,M and q be positive integers,and Q an alphabet with |Q| = q.A set C ={c1,c2,...,cM}(?)Qn is called an(n,M,q)code and each ci is called a codeword.Without loss of generality,we may assume Q = {0,1,...,q-1}.When Q = {0,1},we also use the word "binary".For any CO C C,we define the set of ith coordinates of C0 as For any CO C C,we define the descendant code of C0 asBecause M is the number of legitimate users in a t-(n.,M,q)SMIPPC,we need more code-words when n is given.Let Ms(t,n,q)= max{M | there exists a t-(2,M,q)SMIPPC}.A t-(n,M,q)SMIPPC is said to be optimal if M = Ms(t,n,q).A t-(n,M,g)SMIPPC is said to be asymptotically optimal ifDefinition:Assume that C is an(n,M,q)code.For any CO C C such that 1<|C0|?t.? C is a multimedia identifiable parent property code,denoted by t-(n,M,q)MIPPC,if?c'?Pt(C0)C'?(?)holds,where Pt(C0)={C'(?)C|desc(C')= desc(C0),1? |C'| ? t}.?C is a strong multimedia identifiable parent property code,denoted by t-(n,M,q)SMIPPC,if ?c'?P(c0)C'?(?)holds,where P(C0)= {C'(?)C|desc(C')= desc(C0)}.???In this thesis,the following major results are obtained.Theorem 1 Let C be a(2,M,q)code.C is a t-(2,M,q)SMIPPC if and only if C does not contain the following set where 1 ? i ? t and for any 1? j1,j2?i,aj1?aj2 and bj1?bj2 hold.Theorem 2 There exists a t-(2,M,q)SMIPPC if and only if there exists a bipartite graph G(q,q)with girth at least 2(t + 1),where e(G)= M.Theorem 3 For any t-(2,M,q)SMIPPC,where c is a constant depending only on t.Theorem 4 For any prime power k,there exists an asymptotically optimal 5-(2,M,q)SMIPPC,whereTheorem 5 Let C be a(2,M,q)code.C is a t-(2,M,q)SMIPPC if and only if it is a t-(2,M,q)MIPPC.Theorem 6 Assume that C is a 2-(3,M,q)FPC.C is a 3-(3,M,q)SMIPPC if and only if ? in the following is not a subset of C,where|{ai,bi,ci}| = 3,i = 1,2,3.This thesis is organized as follows:Related definitions and main results are presented in Chapter 1.Based on bipartite graph,an upper bound on Ms(2,M,q)is derived,and an asymptotically optimal t-(2,M,q)SMIPPC is obtained by means of a generalized hexagon in Chapter 2.In Chapter 3,t-(2,M,q)MIPPC and 3-(3,M,q)MIPPC are studied respectively.Finally conclusions and further researches are drawn.