4 citations · 14 across the 12 of their papers we have counts for
9 papers · 1 filter
On cyclotomic nearly-doubly-regular tournaments
Shohei Satake
Nearly-doubly-regular tournaments have played significant roles in extremal graph theory. In this note, we construct new cyclotomic nearly-doubly-regular tournaments and determine…
On the Paley RIP and Paley graph extractor
Shohei Satake
Constructing explicit RIP matrices is an open problem in compressed sensing theory. In particular, it is quite challenging to construct explicit RIP matrices that break the square-…
On high-girth expander graphs with localized eigenvectors
Shohei Satake
The main purpose of this paper is to construct high-girth regular expander graphs with localized eigenvectors for general degrees, which is inspired by a recent work due to Alon, G…
On the restricted isometry property of the Paley matrix
Shohei Satake
In this paper, we prove that the Paley graph conjecture implies that the Paley matrix has restricted isometry property (RIP) beating the square-root bottleneck for the sparsity lev…
On -parent-identifying set systems of block size
Yujie Gu, Shohei Satake
Parent-identifying set system is a kind of combinatorial structures with applications to broadcast encryption. In this paper we investigate the maximum number of blocks …
On expander Cayley graphs from Galois rings
Shohei Satake
In this paper, we study new Cayley graphs over the additive group of Galois rings. First we prove that they are expander graphs by using a Weil-Carlitz-Uchiyama type estimation of…
A constructive solution to a problem of ranking tournaments
Shohei Satake
A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erdős and J. W. Moon. By probabilistic methods, the existence of "unra…
A note on the relation between two properties of random graphs
Shohei Satake
The -e.c. and pseudo-random property are typical properties of random graphs. In this note, we study the gap between them which has not been studied well. As a main result, we g…
On explicit random-like tournaments
Shohei Satake
We give a new theorem describing a relation between the quasi-random property of regular tournaments and their spectra. This provides many solutions to a constructing problem menti…