2007/11/22 by Hurley, Ted
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0711.3629
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.