Related papers: Generating Hadamard matrices with transformers
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Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical…
Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on…
We construct two Hadamard matrices of order 764. Both are of Goethals-Seidel type.
Neural ranking methods based on large transformer models have recently gained significant attention in the information retrieval community, and have been adopted by major commercial solutions. Nevertheless, they are computationally…
An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional…
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Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
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Deep learning has yielded extraordinary results in vision and natural language processing, but this achievement comes at a cost. Most models require enormous resources during training, both in terms of computation and in human labeling…
In this paper we provide a general method to construct four-parameter families of complex Hadamard matrices of order six. Our approach is to write a 6-dimensional matrix as composed of four blocks, each one in the form of a circulant…
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