IJPAM: Volume 50, No. 3 (2009)

CONVOLUTIONAL CODES FROM UNITS IN
MATRIX AND GROUP RINGS

Ted Hurley
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland - Galway
Galway, IRELAND
e-mail: [email protected]


Abstract.A general method for the construction and analysis of convolutional codes from units in Laurent series over matrix rings is presented. Using group rings as matrix rings, this gives a general method for the construction and analysis of convolutional codes from group rings. A theory of group ring convolutional codes is developed. Series of convolutional codes are constructed algebraically and algebraic methods are used to compute free distances and to construct convolutional codes to prescribed minimum distances.

Received: January 7, 2009

AMS Subject Classification: 16S34, 68P30

Key Words and Phrases: convolutional code, group ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 3