This talk will describe some recent work on subspace codes, which were introduced in the context of network coding. Subspace codes allow information to be transmitted over an unknown network even in the presence of errors. In this talk, we give the first explicit construction of list-decodable subspace codes which achieve optimal redundancy.
Our codes are subcodes of Koetter-Kschischang codes, the analogue of Reed-Solomon codes for subspace coding. The construction relies on designing a special class of "subspace designs" suitable for use over large fields. Our techniques also imply the first explicit high-rate list-decodable codes for the rank metric.
Joint work with Venkat Guruswami.