269,505 research outputs found
Construction of Codes for Network Coding
Based on ideas of K\"otter and Kschischang 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 Braun, Kerber
and Laue 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
A Note on the Injection Distance
Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding
for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory,
{54(8), 2008] that the network coding counterpart of Gabidulin codes performs
asymptotically optimal with respect to the subspace distance. Recently, Silva
and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for
Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory,
ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed
picture of what happens in noncoherent network coding. We show that the above
codes are also asymptotically optimal with respect to this distance
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