Linear Code Construct Authentication Codes

Message authencation is an important subject of information security. Authencation code is a subclass of coding theory for message authentication on public channel. In many years, by means of algebra, finite geometry,combinatorial designs and coding theory, a lot of good authentication codes have been constructed. They are valuable for solving the problems in information security.Authentication code in the modern theory model, the information sent to attack the process that there are two types of information posing as a legitimate sender forged false information, known as the impersonation attack .The other is a legitimate sender will distort the message and then send it to the receiver, known as the substitution attack, usually in mind the two attacks were successful and the probability. Authentication code as an important research issue is how to determine these two In the lower bound of probability; Another research topic is the structure can be achieved a number of progressive achievement of these lower bounds or authentication codes. There are two kinds of authencation codes: authencation codes with encrypt function and authencation codes without encrypt function.Recently, codes without encryption have been studied by means of coding theory. In this article,we consider uniform encoding codes in Galois field, and use them to construct new authencation codes. By using certain results, we compute the probabilities P1 and Ps of those new codes,which are important criteria for evaluating the security level of authencation codes.The codes we produced here are all optimal or asymptotic optimal. We compare our codes with results constructed in recent years and find out that when the source state spaces are the same size, our authencation codes use smaller key space to achieve the same security level.