Structure and constructions of cyclic convolutional codes

The encoded sequences of an convolutional code are treated as sequences of polynomials in the ring of polynomials modulo . Any such sequence can then be written as a power series in two variables , where the polynomial coefficient of is the "word" at time unit in the sequence. Necessary and sufficient conditions on the ring "multiplication" for the set of such sequences so that the set becomes alinear associative algebra are derived. Cyclic convolutional codes (CCC\´s)are then defined to be left ideals in this algebra. A canonical decomposition of a CCC into minimal ideals is given which illuminates the cyclic structure. As an application of the ideas in the paper, a number of CCC\´s with large free distance are constructed.