Computing separability elements for the sentence-ambient algebra of split ideal codes

Cyclic structures on convolutional codes are modeled using an Ore extension A[z; sigma] of a finite semisimple algebra A over a finite field F. In this context, the separability of the ring extension F[z] subset of A[z; sigma] implies that every ideal code is a split ideal code. We characterize this separability by means of a being a separable automorphism of the F-algebra A. We design an algorithm that decides if such a given automorphism a is separable. In addition, it also computes a separability element of F[z] subset of A[z; sigma], which is important because it can be used to find an idempotent generator of each ideal code with sentence-ambient A[z; sigma]. (C) 2016 Elsevier Ltd. All rights reserved.