Abstract
In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time.
Acknowledgements
We wish to thank the referees for their valuable comments. This work has been supported by Ministerio de Ciencia e Innovación (Spain) under grant MTM2008-02773.