The predictable degree property, column reducedness, and minimality in multidimensional convolutional coding

Higher-dimensional analogs of the predictable degree property and column reducedness are defined, and it is proved that the two properties are equivalent. It is shown that every multidimensional convolutional code has, what is called, a minimal reduced polynomial resolution. It is uniquely determined (up to isomorphism) and leads to a number of important integer invariants of the code generalizing classical Forney's indices.