2014/11/13 by Cossidente, Antonio, Pavese, Francesco
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1411.3601
An (r,M,2δ;k)q constant--dimension subspace code, δ>1, is a collection \cal C of (k-1)--dimensional projective subspaces of \rm PG(r-1,q) such that every (k-δ)--dimensional projective subspace of \rm PG(r-1,q) is contained in at most a member of \cal C. Constant--dimension subspace codes gained recently lot of interest due to the work by Koetter and Kschischang, where they presented an application of such codes for error-correction in random network coding. Here a (2n,M,4;n)q constant--dimension subspace code is constructed, for every n ≥ 4. The size of our codes is considerably larger than all known constructions so far, whenever n > 4. When n=4 a further improvement is provided by constructing an (8,M,4;4)q constant--dimension subspace code, with M = q12+q2(q2+1)2(q2+q+1)+1.