Prime fuzzy ideals over noncommutative rings
Fuzzy Sets and Systems
| Hi-index | 754.84 |
The encoded sequences of an(n,k)convolutional code are treated as sequences of polynomials in the ring of polynomials moduloX^{n} - 1. Any such sequence can then be written as a power series in two variablesw(X,D), where the polynomial coefficient ofD^{j}is the "word" at time unitjin 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.