27 citations · 76 across the 10 of their papers we have counts for
10 papers
Inconsistency Probability of Sparse Equations over F2
P. Horak, I. Semaev
Let n denote the number of variables and m the number of equations in a sparse polynomial system over the binary field. We study the inconsistency probability of randomly generated…
Connected cubic graphs with the maximum number of perfect matchings
Peter Horak, Dongryul Kim
It is proved that for , the number of perfect matchings in a simple connected cubic graph on vertices is at most , with being the -th Fibonacci n…
50 Years of the Golomb--Welch Conjecture
Peter Horak, Dongryul Kim
Since 1968, when the Golomb--Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast lit…
Algebraic Method in Tilings
Peter Horak, Dongryul Kim
In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling -space by translate…
A Combinatorial Problem Related to Sparse Systems of Equations
Peter Horak, Igor Semaev, Zsolt Tuza
Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, o…
Speeding up Deciphering by Hypergraph Ordering
Peter Horak, Zsolt Tuza
The "Gluing Algorithm" of Semaev [Des.\ Codes Cryptogr.\ 49 (2008), 47--60] --- that finds all solutions of a sparse system of linear equations over the Galois field --- ha…