---
title: Construction of Minimal Tail-Biting Trellises for Codes over Finite Abelian Groups
url: https://www.emergentmind.com/papers/0702020
type: paper
arxiv_id: '0702020'
arxiv_url: https://arxiv.org/abs/0702020
published: '2007-02-05'
categories:
- cs.IT
- math.IT
---

# Construction of Minimal Tail-Biting Trellises for Codes over Finite Abelian Groups

## Abstract

A definition of atomic codeword for a group code is presented. Some properties of atomic codewords of group codes are investigated. Using these properties, it is shown that every minimal tail-biting trellis for a group code over a finite abelian group can be constructed from its characteristic generators, which extends the work of Koetter and Vardy who treated the case of a linear code over a field. We also present an efficient algorithm for constructing the minimal tail-biting trellis of a group code over a finite abelian group, given a generator matrix.