Some Properties of Maximum Length Cellular Automata

  • Cho, Sung-Jin (Dept. of Applied Mathematics, Pukyong National University) ;
  • Kim, Han-Doo (Dept. of Mathematics, Inje University) ;
  • Choi, Un-Sook (Dept. of Applied Mathematics, Pukyong National University)
  • Published : 1999.12.31

Abstract

In this paper, We consider two-dimensional Maximum Length Cellular Automata (2-D MLCA) as an extension of the 1-D MLCA. 2-D MLCA can display much better random patterns than those generated by 1-D CA and LFSR. To generate random pattern, a CA should have a maximum length cycle. So, it is necessary to find MLCA that the characteristic polynomial of the transition matrix is primitive. New boundary conditions of 3 types are proposed and some rules having primitive polynomials of 2-D MLCA are found.

Acknowledgement

Supported by : Ministry of Information and Communications