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Abstract
We investigate the structure of the code graph of a multicast network that has a
characteristic shape of an inverted equilateral triangle. We provide a criterion that
determines the validity of a receiver placement within the code graph, present
invariance properties of the determinants corresponding to receiver placements under
symmetries, and provide a complete study of these networks’ receivers and required
field sizes up to a network of four sources. We also improve on various definitions
related to code graphs.
Keywords
multicast network, triangular semilattice, determinantal
condition, finite field, multivariate polynomial, linear
network coding, multicast communication, code graph
Mathematical Subject Classification 2010
Primary: 68P30, 68R10
Secondary: 11T06
Milestones
Received: 14 January 2019
Revised: 3 July 2019
Accepted: 31 August 2019
Published: 25 October 2019
Communicated by Nigel Boston