Construction of Codes for Network Coding

Based on ideas of Kötter and Kschischang [6] we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in [1] as a purely combinatorial object. For the construction of network codes we successfully modified methods (construction with prescribed automorphisms) originally developed for the q-analogues of a combinatorial designs. We then give a special case of that method which allows the construction of network codes with a very large ambient space and we also show how to decode such codes with a very small number of operations. network coding, q-analogue of Steiner systems, subspace codes, constant dimension subspace codes, decoding, Singer cycle