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An Efficient Algorithm for Constructing Minimal Trellises for Codes over Finite Abelian Groups (1996)
| Citations: | 19 - 2 self |
BibTeX
@MISC{Vazirani96anefficient,
author = {Vijay V. Vazirani and Huzur Saran and B. Sundar Rajah},
title = {An Efficient Algorithm for Constructing Minimal Trellises for Codes over Finite Abelian Groups},
year = {1996}
}
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Abstract
We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a generator matrix for the code. We also show how to cornpure a succinct representation of the minimal trellis for such a code, andpresent algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine, who handled the case of linear codes over fields. An important application of our algorithms is to the construction qf minireal trellises for lattices. A key step in our work is handling codes over cyclic groups C'p, where p is a prime. Such a code can be viewed as a submodule over the ring Zp. Because of the presence of zero-divisors in the ring, submodules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to p-linear combination, and introducing the notion of a p-generator equence, which enjoys properties similar to that of a generector matrix for a vector space.
Keyphrases
finite abelian group efficient algorithm minimal trellis constructing minimal trellis vector space generector matrix key step succinct representation p-generator equence group code ring zp linear combination p-linear combination linear code useful property andpresent algorithm local description construction qf minireal trellis cyclic group important application generator matrix
