Open AccessOn achievability of an ( r , l ) fractional linear network code
Author(s) -
Das Niladri,
Rai Brijesh Kumar
Publication year - 2017
Publication title -
iet networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.466
H-Index - 21
ISSN - 2047-4962
DOI - 10.1049/iet-net.2016.0094
Subject(s) - mathematics , scalar (mathematics) , dimension (graph theory) , integer (computer science) , discrete mathematics , combinatorics , code (set theory) , computer science , geometry , programming language , set (abstract data type)
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 .