On Constructions Of Symbol-pair Codes And Their Related Properties

In information theory,noisy channels are analyzed generally by dividing the message into independent information units.With the development of modern high-density data storage systems,the reading process may be lower than that of the process used to store the data.Motivated by this situation,symbol-pair codes are proposed by Cassuto and Blaum in 2010 to protect against pair-errors over symbol-pair read channels.The minimum symbol-pair distance plays an important role in determining the error-correcting capability of a symbol-pair code.Maximum dis-tance separable(MDS)symbol-pair codes and almost maximum distance separable(AMDS)symbol-pair codes are optimum and sub-optimum regarding to the Single-ton bound,respectively.The classical MDS codes are MDS symbol-pair codes.The purpose of this dissertation is mainly to study the constructions of MDS symbol-pair codes and AMDS symbol-pair codes,the symbol-pair weight distribution of MDS codes and the b-symbol weight distribution of simplex codes.The main results are as follows:On the one hand,five classes of MDS symbol-pair codes are proposed by virtue of repeated-root cyclic codes over Fp in this dissertation.For n=3p,we construct two classes of MDS symbol-pair codes process minimum symbol-pair distance ten or twelve,which is bigger than all the known MDS symbol-pair codes from constacyclic codes.Next,for length n=4p,one derives a class of MDS symbol-pair codes with dp=7,which generalizes the result in[28].And for n=5p,two classes of MDS symbol-pair codes with minimum symbol-pair distance seven and eight are presented.In addition,five new classes of AMDS symbol-pair codes with dp ?{4,6,7,8,10} from repeated-root cyclic codes are deduced and one class of such codes has unbounded lengths.As our best knowledge,it is the first time for the explicit construction of AMDS symbol-pair codes.On the other hand,in this dissertation,we investigate the symbol-pair weight distribution of the classical MDS codes and the b-symbol weight distribution of simplex codes over finite fields respectively.Utilizing shortened codes and the Ham-ming weight distribution of the classical MDS codes,we characterize the symbol-pair weight distribution of the classical MDS codes.By analyzing the intersection of certain hyperplanes,the symbol-pair weight distribution of simplex codes is ob-tained.Notably,by rearranging coordinates in simplex codes,one may obtain differ-ent symbol-pair weights.Furthermore,the b-symbol weight distribution of variation simplex codes over certain finite fields is determined.Precisely,for any m>1,the p-symbol weight of codewords in variation simplex codes over Fpm and for any odd b with 3?b?3m-1,the b-symbol weight of codewords in variation simplex codes over F3m are derived respectively.