Bent functions on a Galois ring and systematic authentication codes

Introduction On a public communication channel there is a risk that an intruder can deliberately observe and even cause a disturbance in the communication. An authentication code provides a method for insuring the integrity of the information to be sent through this channel. These codes, first introduced by Gilbert, MacWilliams and Sloane, have since received attention by several authors and may be with secrecy and without secrecy; a subclass of the latter is the Systematic Authentication Codes (SACs). Several types of SACs have been constructed using various concepts such as highly nonlinear functions over finite fields or non-degenerated and rational functions on a Galois ring . By introducing a class of bent functions over a Galois ring of characteristic p2, (p a prime) and using the Gray map on such ring, a class of SACs is presented and an example is given to illustrate the main results.