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We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [19, 22]. Codes of this type are described as submodules of F[z] with some additional… (More)

- Andre Hillebrand, Wiland Schmale
- J. Symb. Comput.
- 2001

Simplifying a matrix of differential operators by elementary row and column operations is quite a fundamental task. If one considers matrices whose entries are ordinary timevarying differential… (More)

After a discussion of the Griesmer and Heller bound for the distance of a convolutional code we present several codes with various parameters, over various fields, and meeting the given distance… (More)

- Naoharu Ito, Wiland Schmale, Harald K. Wimmer
- SIAM J. Control and Optimization
- 2000

For discrete-time linear systems over a principal ideal domain three types of (C; A)-invariance can be distinguished. Connections between these notions are investigated. For pure submodules necessary… (More)

- Heide Gluesing-Luerssen, Wiland Schmale
- Applicable Algebra in Engineering, Communication…
- 2006

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra $$\mathbb{F}[x]/(x^n-1)$$ , where $$\mathbb{F}$$ is a finite field. A particular choice of the data leads… (More)

- H. Cluesing-Luerssen, Barbara Langfeld, Wiland Schmale
- International Symposium onInformation Theory…
- 2004

This paper describes the powerful theory of cyclic block codes, which suggests studying the impact of cyclicity for convolutional codes. The convolutional codes, which are invariant under the cyclic… (More)

- Heide Gluesing-Luerssen, Wiland Schmale, Melissa Striha
- 2002

In this note we will construct and investigate some small cyclic convolutional codes. Among other things we will present an infinite series of one-dimensional CCCs over F4 with length 3 and… (More)

The 22-year-old conjecture is addressed which claims that any reachable matrix pair (A,B) from C[x]n×(n+m) is cyclizable, i.e. allows for F, u over C[x] s.t. (A + BF)kBu, k = 0, . . . , n − 1, is a… (More)

- Heide Gluesing-Luerssen, Wiland Schmale
- Proceedings. International Symposium on…
- 2005

In this paper we introduce a specific class of cyclic convolutional codes. The construction is based on Reed-Solomon block codes. The algebraic parameters as well as the distance of these codes are… (More)

- Jim Brewer, Wiland Schmale
- 1999

An (A,B)-cyclic submodule M is generated by the states of one single trajectory of a linear control system whose parameters come from a commutative ring. M is “finite”, when it is generated by the… (More)