Several formulations for the definition of a multidimensional convolutional code are discussed in a symbolic dynamics setting and then one is adopted. Using this definition it is shown that there are five other equivalent formulations. One is in terms of the dual space of linear functionals, one is in terms of a parity check system, one is in terms of an algebraic conjugacy, another is in terms of a convolutional encoder, and the last is in terms of a convolutional decoder. Finally, two examples of two-dimensional convolutional codes are discussed in detail.

The state splitting algorithm of Adler, Coppersmith, and Hassner for graphs with edges of fixed length is extended to graphs with edges of variable lengths. This has the potential to improve modulation code construction techniques. Although the ideas of state splitting come from dynamical systems, completely graph-theoretic terms are used.