The Applications Of Coding Theory In Some Fields

Communication is to make the receiver obtain information at the first time, and to ensure the confidentiality of the message. But in the actual digital communication system, the accuracy of the message and transmission speed is contradictory. So how to solve the contradiction between the both, is the content of the coding theory research. Since the born of theory about error correction code, it got the attention of many researchers, in a relatively short period,which had got a rapid development,constantly improve its theory, and applied to all aspects of life. Mainly used in cryptography, DNA computing and quantum error correcting code, etc.This paper will offer several applications in the field of DNA computing and quantum error-correcting code, and give the method of their structure as a one-to one mapping and CSS construction, then achieve a better code than ever. This paper mainly do the following two aspects.1. According to DNA computing, in present, the studies have designed the effective methods such as DNA Golay coding to ensure the success rate of DNA computing. The third chapter firstly instruct binary Hamming code through a one-to-one mapping, a classic of the error correcting code is applied to DNA computing, and the new generation of DNA code word has some special properties. Mostly, several specific examples are given and analyzed.2. Aimming at the problem of the quantum error-correcting code affected by some sudden factors in the actual transmission process, previous researches have proved some construction methods depend on the quantum error-correcting code. As it is well-known, quantum burst-correcting codes provide the most efficient way to overcome quantum bursts of errors. In this paper, we present a new approach for constructing quantum burst-correcting codes.The key point of the proposed approach is to construct linear codes C1=[[n,k,d]]1 and BCH codes C2=[n,k2,d2]1 withC11(?)C2 Furthermore, product codes (C1(?)C2)1 and C,(?)C2 can be constructed. Subsequently quantum burst-correcting product codes with parameters [[n2,n2-n] can be constructed easily. In addition, we can give the ability of the quantum burst-correcting codes.