On achievability of an (r, l) fractional linear network code. Issue 3 (1st May 2017) - Das, Niladri; Rai, Brijesh Kumar
Abstract : It is known that there exists a network, called as the M‐network, which is not scalar linearly solvable but has a vector linear solution for message dimension two. Recently, a generalisation of this result has been presented where it has been shown that for any integer m ≥ 2, there exists a network which has an ( m, m ) vector linear solution, but does not have a ( w, w ) vector linear solution for w < m . This study presents a further generalisation. Specifically, the authors show that for any positive integers k, n, and m ≥ 2, there exists a network which has a ( mk, mn ) fractional linear solution, but does not have a ( wk, wn ) fractional linear solution for w < m .