Several Classes Of Optimal Ternary Cyclic Codes With Minimal Distance Four

Error correcting code theory is an important part of information theory,which can effectively improve the reliability of information transmission.As an important subclass of linear codes,cyclic codes are an important subclass of linear codes and have wide applications in consumer electronics,data storage systems and communication systems,since they have special algebraic structure and efficient encoding and decoding algorithms.In recent years,an important topic in coding theory is the construction of optimal cyclic codes,especially the study of the optimality of cyclic codes generated by a few zeros.In this paper,we will present a Basic Theorem about the optimal ternary cyclic codesC_u,v.And four classes of optimal ternary cyclic codesC_1,v,two classes of opti-mal ternary cyclic codesC_u,vwith parameters[3^m-1,3^m-1-2m,4]for some suitable values of,are gave by determining the solutions of certain equations.Specifically,the experimental data show that the five classes of optimal ternary cyclic codes pro-posed in this paper are not equivalent to all known results,that is,the five classes of optimal cyclic codes proposed in this paper are novel,while the non-equivalence be-tween the other class of optimal cyclic codes and known results needs to be further studied.