2016/06/19 by Niladri Das, Das, Niladri, Brijesh Kumar Rai +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1606.05904
arxiv created 2016/06/19 · arxiv updated 2016/06/21
It is known that there exists a network which does not have a scalar linear solution over any finite field but has a vector linear solution when message dimension is 2 [3]. It is not known whether this result can be generalized for an arbitrary message dimension. In this paper, we show that there exists a network which admits an m dimensional vector linear solution, where m is a positive integer greater than or equal to 2, but does not have a vector linear solution over any finite field when the message dimension is less than m.