As we know from cyclic codes, they can be represented by polynomials, from which we derive the encoding or decoding matrix. From that polynomial representation, we can extend them to convolutional
codes. Indeed, as the polynomial representation of convolutional codes allows us to benefit from the linear systems theory, we will be looking at such an extension of convolutional cyclic codes as linear
systems to use the linear systems properties, as quaternary codes looking into the Z4 ring.