On Field Size and Success Probability in Network Coding

  • Olav Geil
  • Ryutaroh Matsumoto
  • Casper Thomsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5130)


Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.


Distributed networking linear network coding multicast network coding random network coding 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Olav Geil
    • 1
  • Ryutaroh Matsumoto
    • 2
  • Casper Thomsen
    • 1
  1. 1.Department of Mathematical SciencesAalborg UniversityDenmark
  2. 2.Department of Communications and Integrated SystemsTokyo Institute of TechnologyJapan

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