On doubly-cyclic convolutional codes

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra [x]/(xⁿ-1), where is a finite field. A particular choice of the data leads to the class of doubly-cyclic CC's. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC's basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.