On Doubly-Cyclic Convolutional Codes

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra $$\mathbb{F}[x]/(x^n-1)$$, where $$\mathbb{F}$$ 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.

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