AN EFFICIENT ALGORITHM FOR CONSTRUCTING MINIMAL TRELLISES FOR CODES OVER FINITE ABELIAN-GROUPS

We present an efficient algorithm for computing the minimal trellis fo r a group code over a finite abelian group, given a generator matrix f or the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use t his information to compute efficiently local descriptions of the minim al trellis. This extends the work of Kschischang and Sorokine, who tre ated the case of linear codes over fields, An important application of our algorithms is to the construction of minimal trellises for lattic es. A key step in our work is handling codes over cyclic groups C-p al pha, where p is a prime. Such a code can be viewed as a module over th e ring Z(p) alpha. Because of the presence of zero divisors in the rin g, modules do not share the useful properties of vector spaces, We get around this difficulty by restricting the notion of linear combinatio n to a p-linear combination, and by introducing the notion of a p-gene rator sequence, which enjoys properties similar to those of a generato r matrix for a vector space.