High-girth Steiner triple systems Page 1 Annals of Mathematics 200 (2024), 1059–1156
https://doi.org/10.4007/annals.2024.200.3.4 High-girth Steiner triple systems By Matthew Kwan …

This article develops a general method for constructing entanglement-assisted quantum low-
density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit …

The resolution of the antiâ•’Pasch conjecture Page 1 The Resolution of the Anti-Pasch
Conjecture MJ Grannell,1 TS Griggs,1 and CA Whitehead2 1Department of Pure Mathematics …

Four methods for constructing anti-Pasch Steiner triple systems are developed. The first
generalises a construction of Stinson and Wei to obtain a general singular direct product …

This paper extends the class of low-density parity-check (LDPC) codes that can be
algebraically constructed. We present regular LDPC codes based on resolvable Steiner 2 …

Recent breakthroughs in forward error correction, in the form of low-density parity-check
(LDPC) and turbo codes, have seen the promise of near Shannon limit information …

A hypergraph is called an r× rgrid if it is isomorphic to a pattern of r horizontal and r vertical
lines, ie, a family of sets {A1,…, Ar, B1,…, Br} such that Ai∩ Aj= Bi∩ Bj= 0̸ for 1≤ i< j≤ r …

Abstract Properties of the 11$\, $084 $\, $874 $\, $829 Steiner triple systems of order 19 are
examined. In particular, there is exactly one 5-sparse, but no 6-sparse, STS (19); there is …

Reliability is a major concern in the design of large disk arrays. Hellerstein et al. pioneered
the study of erasure-resilient codes that allow one to reconstruct the original data even in the …

We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such
systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then …