| The algebraic coding theory is closely related to many important subjects such as mathematics,cryptography and computer science,and the error correcting coding theory is one of the most important research fields in the theory of algebraic coding.Since the50s of last century,a class of very important error correcting codes-binary cyclic codes have attracted the attention of scholars.A.R.Hammons and other scholars devoting themselves into studying the codes on the Z4 ring.After this,a class of new codes have attracted people's attention.This code is called Z2 Z4-additive cyclic code.This code has a good characteristic is that it can be regarded as a class of binary code under the Gray map.Based on this,it provide convenient to coding and decoding of this codes.The research on this codes become a hot spot in recent years.In this paper,based on the Z2 Z4-additive cyclic codes theory and the existing results.As for a further comment we extend the research of Z3 Z9-additive cyclic codes.In Chapter 1,we first briefly review the development process of algebraic coding theory,and then introduce some basic knowledge of codes.In Chapter 2,the definition of Z3?Z9?-additive cyclic code is given.The third chapter is the main part of this paper.First,we give the definition of Z3 Z9-additive cyclic code and calculate the minimum generating set of the Z3 Z9-additive cyclic code.Secondly,we define the dual of the Z3 Z9-additive cyclic code.By establishing the orthogonal relationship on Z3 Z9,its dual is still a negacyclic codes can be proved.And the generating matrix is given.Finally,we give the generaters of dual codes by constructive methods which can bring convenience to the calculation and application of the elements of codes. |
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