Synthesis of all Maximum Length Cellular Automata of Cell Size up to 12

Maximum length CA has wide range of applications in design of linear block code, cryptographic primitives and VLSI testing particularly in Built-In-Self-Test. In this paper, an algorithm to compute all $n$-cell maximum length CA-rule vectors is proposed. Also rule vectors for each primitive polynomial in GF(2^2) to GF(2^{12} have been computed by simulation and they have been listed.Programmable rule vectors based maximum length CA can be used to design cryptographic primitives.