Leírás
Free distance is, probably, the most fundamental parameter of a
convolutional code, but its computation is expensive. A procedure for its
calculation is to get an increasing sequence of lower bounds (the column
distance sequence) which, in the limit, reaches the free distance. When the
convolutional code is endowed with an adequate cyclic structure, an adapted
column distance sequence, with a more regular behavior than the classical
one, will be constructed. To this end, an idempotent generator of the code
is needed, so that a basic question is whether such an idempotent do exists
for a given cyclic convolutional code. We will show how to use a separable
ring extension to solve this problem. These results have been obtained in
collaboration with F. J. Lobillo and G. Navarro, from the University of
Granada. The initial minutes of the talk will be devoted to introduce the
notion of convolutional code, free distance and classical column distance
sequence.