6 papers
The Weight Distribution of the Third-Order Reed-Muller Code of Length 2048
Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta
We compute the weight distribution of the third-order Reed--Muller code RM(3,11) of length 2048. The weight enumerator is assembled from the coset weight enumerators of f+RM(2,10),…
Classification of Boolean Cubic Forms in Ten Variables
Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta
We classify Boolean cubic forms in ten variables up to GL(10,2)-equivalence. The catalog contains all 3691560 nonzero orbits. For every orbit we provide a representative with small…
Tensor Decomposition for Non-Clifford Gate Minimization
Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta
Fault-tolerant quantum computation requires substantial resources for non-Clifford gates. Their count also enters exponentially into the runtime of several classical simulation met…
Faster Algorithms for Structured Matrix Multiplication via Flip Graph Search
Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta
We give explicit low-rank bilinear non-commutative schemes for multiplying structured matrices with , which serve as building blocks for recursive alg…
A Machine Learning Approach That Beats Large Rubik's Cubes
Alexander Chervov, Kirill Khoruzhii, Nikita Bukhal +9
The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural ne…
CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs
A. Chervov, M. Obozov, A. Soibelman +31
This paper is the second in a series of studies on developing efficient artificial intelligence-based approaches to pathfinding on extremely large graphs (e.g. nodes) wit…