Convolutional codes from units in matrix and group rings [article]

Ted Hurley
2007 arXiv   pre-print
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.
arXiv:0711.3629v1 fatcat:c7hixzjhwbbfth572ytjidll4a