MacWilliams identities for terminated convolutional codes

Abstract

Shearer and McEliece showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear convolutional code C and its orthogonal code C[superscript ⊥], and that this distribution is as useful as the free distance spectrum for estimating code performance. These observations are similar to those made recently by Bocharova et al.; however, we focus on terminating by tail-biting rather than by truncation.