6 citations · 6 across the 5 of their papers we have counts for
5 papers
More results on the number of zeros of multiplicity at least r
Olav Geil, Casper Thomsen
We consider multivariate polynomials and investigate how many zeros of multiplicity at least they can have over a Cartesian product of finite subsets of a field. Here r is any…
Weighted Reed-Muller codes revisited
Olav Geil, Casper Thomsen
We consider weighted Reed-Muller codes over point ensemble where needs not be of the same size as . For we determine optimal weights an…
List decoding of a class of affine variety codes
Olav Geil, Casper Thomsen
Consider a polynomial in variables and a finite point ensemble . When given the leading monomial of with respect to a lexicographic orderin…
On the number of zeros of multiplicity r
Olav Geil, Casper Thomsen
Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicit…
On Field Size and Success Probability in Network Coding
Olav Geil, Ryutaroh Matsumoto, Casper Thomsen
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 line…