New convolutional code constructions and a class of asymptotically good time-varying codes

We show that the generator polynomials of certain cyclic codes define noncatastrophic fixed convolutional codes whose free distances are lowerbounded by the minimum distances of the cyclic codes. This result is used to construct convolutioual codes with free distance equal to the constraint length and to derive convolutional codes with good free distances from the BCH codes. Finally, a class of time-varying codes is constructed for which the free distance increases linearly with the constraint length.