  In this paper, we present an algebraic construction of tail-biting trellises.
The proposed method is based on the state space expressions, i.e., the state
space is the image of the set of information sequences under the associated
state matrix. Then combining with the homomorphism theorem, an algebraic
trellis construction is obtained. We show that a tail-biting trellis
constructed using the proposed method is isomorphic to the associated
Koetter-Vardy (KV) trellis and tail-biting Bahl-Cocke-Jelinek-Raviv (BCJR)
trellis. We also evaluate the complexity of the obtained tail-biting trellises.
On the other hand, a matrix consisting of linearly independent rows of the
characteristic matrix is regarded as a generalization of minimal-span generator
matrices. Then we show that a KV trellis is constructed based on an extended
minimal-span generator matrix. It is shown that this construction is a natural
extension of the method proposed by McEliece (1996).
