Combinatorial Batch Codes Based On RTD(q-2.q)

Batch codes were introdHced by Ishai,Kushilevitz,Ostrovsky and Sahai in 2004, batch codes specifry a method to resolve problem abont information retrieval,the question is how to distribute a database of n items among servers in suchh a way that when we need any κ items among the n items,we can read at most t items froml each server to retrieve them,and we want the total storage N as small as possible. After the data distribution.if we treat each server as a subset of the set of n items，we call these codes s combinatorial batch codes，we only study the special case t＝1,a combinatorial batch code with parameters n,k,m is denoted by(n,N,κ,m)-CBC.We say that an (n,N,κ,m)-CBC is optimal if N≤N’for all(n,N’,κ,m)-CBC and we denote the corresponding value of N by N(n,κ,m).For given n,κ,m,the optimal value of CBC is still not fully sure for n<(k-2m).When n<(k-2m),a new construction of(q2+q-2,q3-q2-2q,q2-2q-16,q2-2q)-CBc based on BTD(q-2,q)is presented in this paper,a reasonable method for distributing a database of q2+q-2 items among q2-2q servers is presented in this paper.For given n=q2+q-2, κ=q2-2q-16,m=q2-2q,existing construction(m+p,m+p+ε+E(κ,p),κ,m)-CBC can not deterrmin the value of N；existing construction(κ+s+d,2κ+2s+(d-1)p-b,κ,κ+s)CBC can determin the value of N is 3gq3-7q2-46g+32；our construction can determine the value of N is q3-q2-2q．By comparison，our construction is superior to the existing constructions(κ+s+d,2κ+2s+(d-1)p-b,κ,κ+s)-CBC.