English

Symmetric Unique Neighbor Expanders and Good LDPC Codes

Combinatorics 2016-05-11 v1

Abstract

An infinite family of bounded-degree 'unique-neighbor' expanders was constructed explicitly by Alon and Capalbo (2002). We present an infinite family F of bounded-degree unique-neighbor expanders with the additional property that every graph in the family F is a Cayley graph. This answers a question raised by Tali Kaufman. Using the same methods, we show that the symmetric LDPC codes constructed by Kaufman and Lubotzky (2012) are in fact symmetric under a simply transitive group action on coordinates.

Keywords

Cite

@article{arxiv.1605.00240,
  title  = {Symmetric Unique Neighbor Expanders and Good LDPC Codes},
  author = {Oren Becker},
  journal= {arXiv preprint arXiv:1605.00240},
  year   = {2016}
}
R2 v1 2026-06-22T13:45:43.976Z