English

On Field Size and Success Probability in Network Coding

Information Theory 2008-09-04 v1 math.IT

Abstract

Using tools from algebraic geometry and Groebner 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.

Keywords

Cite

@article{arxiv.0806.4510,
  title  = {On Field Size and Success Probability in Network Coding},
  author = {Olav Geil and Ryutaroh Matsumoto and Casper Thomsen},
  journal= {arXiv preprint arXiv:0806.4510},
  year   = {2008}
}

Comments

16 pages, 3 figures, 2 tables. Accepted for publication at International Workshop on the Arithmetic of Finite Fields, WAIFI 2008

R2 v1 2026-06-21T10:55:02.458Z