The Construction Of MDS Symbol-pair Codes On F_P

Symbol pair codes are designed to protect against pair-errors in data reading channels.The minimum pair-distance is an important parameter to measure the ability of correcting pair-errors.Given code lengths and code sizes,maximum Distance Separable(MDS)symbol-pair codes are optimal in the sense that minimum pair-distance is the greatest.The most important problem of symbol-pair codes is to construct MDS symbolpair codes with larger code length and larger minimum pair-distance.In this dissertation,we propose the relationship between Hamming distance and pair-distance of linear codes on the basis of linear codes,cyclic codes and repeat-root codes.Besides,we analyze the common methods of constructing MDS symbol-pair codes and construct some new MDS symbol-pair codes with length of 2p and minimum pair-distances of 5,6,7 and 8 by using repeated-root codes.In addition,the MDS symbol-pair codes with equal distance are expressed in a unified form.Then we give examples of minimum symbol-pair of 9 and 10 and the related conjectures.We also construct MDS symbolic-pair codes with minimum pair-distance of 2p on the relationship between MDS symbol-pair codes and almost Maximum Distance Separable codes.On one hand,we extend the minimum pair-distance of symbol-pair codes to 2p.On the other hand,we expand the types of MDS symbol-pair codes and solve the problem of the small minimum pair-distance to a certain extent.