The Construction of A-Code from Projective Spaces over Finite Fields

A3-code has a dishonest arbiter who may disturb the communication compared with A2-code, and the arbiter also has some secret key information used to arbitrate in the case of dispute between the senders and receivers. This paper firstly introduces the model of A3-code and the seven types of possible cheating attacks as well as their computational formula. And then a construction of A3-code is presented using the incidence relation of flats from projective spaces over finite fields. The parameters of the code and the probabilities of success in different attacks are also computed, assuming that the probability distributions of source states and participants keys are uniform. Key–Words: A3-codes, projective spaces , finite fields.