On Doubly-Cyclic Convolutional Codes: MSC (2000)

  • Authors:

  • Heide Gluesing-Luerssen;Wiland Schmale

  • Affiliations:

  • Department of Mathematics, University of Groningen, P. O. Box 800, 9700, AV Groningen, The Netherlands;Department of Mathematics, University of Oldenburg, 26 111, Oldenburg, Germany

  • Venue:
  • Applicable Algebra in Engineering, Communication and Computing
  • Year:
  • 2006

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Abstract

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 to the class of doubly-cyclic CC’s. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC’s, basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.