On the Gap between Scalar and Vector Solutions of Generalized Combination Networks

2020/01/13 by Hedongliang Liu, Hengjia Wei, Liu, Hedongliang +7 · 2 citations
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Information Theory (cs.IT) #Interconnection Networks and Systems #Probability (math.PR) #Social and Information Networks (cs.SI) #VLSI and FPGA Design Techniques #cs.IT #cs.SI #math.CO #math.IT #math.PR

paper · pdf · doi:10.48550/arxiv.2001.04150

6 pages, 1 figures, accepted by ISIT 2020, revised according to the reviews

openalex publication_date 2020/01/13 · arxiv created 2020/05/12 · arxiv updated 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study scalar-linear and vector-linear solutions to the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a general lower bound on the gap in the alphabet size between scalar-linear and vector-linear solutions.

Cited by

• On the Gap between Scalar and Vector Solutions of Generalized Combination Networks
• On the Minimum Field Size of Network MDS Codes for Generalized Combination Networks

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