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Shearer and McEliece [1977] showed that there is no MacWilliams identity forthe free distance spectra of orthogonal linear convolutional codes. We showthat on the other hand there does exist a MacWilliams identity between thegenerating functions of the weight distributions per unit time of a linearconvolutional code C and its orthogonal code C^\perp, and that thisdistribution is as useful as the free distance spectrum for estimating codeperformance. These observations are similar to those made recently byBocharova, Hug, Johannesson and Kudryashov; however, we focus on terminating bytail-biting rather than by truncation.

MacWilliams Identities for Terminated Convolutional Codes