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Convolutional codes from units in matrix and group rings (0711.3629v1)
Published 22 Nov 2007 in cs.IT, math.IT, and math.RA
Abstract: A general method for constructing convolutional codes from units in Laurent series over matrix rings is presented. Using group ring as matrix rings, this forms a basis for in-depth exploration of convolutional codes from group ring encoding, wherein the ring in the group ring is itself a group ring. The method is used to algebraically construct series of convolutional codes. Algebraic methods are used to compute free distances and to construct convolutional codes to prescribed distances.