On achievability of an (r, l) fractional linear network code. Issue 3 (1st May 2017)

• Record Type: Journal Article
• Authors: Das, Niladri; Rai, Brijesh Kumar
• Is Part Of: IET networks. Volume 6:Issue 3(2017)
• Page Start: 54
• Page End: 61
• Publication Date: 2017-05-01
• Subjects: linear codes; fractional linear network code -- M‐network -- vector linear solution; Computer network architectures -- Periodicals; Computer network protocols -- Periodicals; Information networks -- Periodicals; Telecommunication systems -- Periodicals; 004.605
• DOI: 10.1049/iet-net.2016.0094
• Languages: English
• ISSNs: 2047-4954

Abstract

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 .