New Classes Of Authentication Codes From Linear Codes

In this thesis we will apply algebraic method to study problems in secure com-munication and related topics.We are working on finite fields,number theory,infor-mation and coding theory to construct some authentication codes.The construction is generalization of some known ones.Within the framework of the generic construction,several classes of authentication codes using certain classes of error-correcting codes are described.In this thesis we will introduce several classes of cyclic codes to construct authentication codes.For these constructions,we have three participants:transmitter,a receiver and an opponent.We assume that the opponent defines two kind of attacks in the mes-sage sending process such as the impersonation attack and the substitution attack.Our constructions can resist those attacks efficiently.