Some Study On Single Error Correcting Codes Of Limited Magnitude

This thesis mainly study the asymmetric or symmetric single error correcting codes of limited magnitude over the residue class ring Zq by constructing the packing sets(B1[?](q)sets?B1[±?](g)sets).In the introduction part and Chapter 1,we introduce the background and some basic knowledge.In Chapter 2,some results of asymmetric single error correcting codes of limited magnitude over Z2kr are presented.We reduce the construction of a maximal size B1[4](2kr)set for k? 3 to the construction of a maximal size B1[4](2k-3r)set.An explicit construction of maximal size B1[4](4r)set is given.Also,we give the partition of Z2kr and discuss the lower bounds of maximal size of B1[4](zr)set by using the cyclotomic coset.Moreover,we conjecture that those lower bounds are tight by computer searching.In Chapter 3,for gcd(r,6)=1.the recursive relationship of maxinial size B1[4](2a3br)set and maximal size B1[4])2a-33br)set are given.In this sense it suffices to consider maximal size B1[4](4·3br)set,B1[4](2·36r)set and B1[4](3br)set.In the case a=0,the maximal size B1[4](3br)set.has been studied in[18]when b?2.For b=1,we give an explicit construction of maximal size B1[4](3r)set.Finally,the maximal size B1[4](12r)ser and B1[4](2·3br)set are considered.The construction of maximal size B1[4](3br)sets is an open problem.Chapter 4 is devoted to the connection between the symmetric single error correcting codes of limited magnitude and the equal difference avoidable conflict codes.Direct constructions for tight or quasi-tight equal difference avoidable conflict codes of specific length are considered.In Chapter 5,we summarize this thesis and present some further research problems.