Geometrically Uniform n-shot Subspace Codes

In [A. Khaleghi, D. Silva, and F.R. Kschischang, Subspace Codes, Lecture Notes in Computer Science, vol. 5921, pp. 1-21, 2009] it is proposed an efficient error-control procedure for use in Network Coding called subspace codes constructed from projective space of order m over a finite field Fq, denoted by P(Fqm), that is, the set of all subspaces in the vector space Fqm, [T. Etzion, and A. Vardy, Error Correcting Codes in Projective Space, Proc. of the 2008 IEEE Int. Symp. on Inf. Theory, 871-875, Toronto, Canada, 2008]. The projective space endowed with the subspace metric is a metric space. Such subspace codes are devised for the one use of the channel. An alternative to improve the rate and the error-correcting capabilities, without increasing the order of the finite field or the vector length, is to make use of the channel n times, this new code is known as the n-shot subspace code, [R. Nóbrega, and B. Uchôa-Filho, Multishot Codes for Network Coding: Bounds and a Multilevel Construction, Proc. of the 2009 IEEE Int. Symp. on Information Theory - ISIT-09, Seoul, South Korea, Jun. 2009]. In this paper we present the concept of geometrically uniform subspace codes and the new n-shot geometrically uniform subspace codes.