Convolutional codes from units in matrix and group rings

A general method for the construction and analysis of convolu- tional 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.

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