A Family of Two-Weight Ring Codes and Strongly Regular Graphs Cover Image

A Family of Two-Weight Ring Codes and Strongly Regular Graphs
A Family of Two-Weight Ring Codes and Strongly Regular Graphs

Author(s): Ivan Landjev, Stoyan Boev
Subject(s): Education, ICT Information and Communications Technologies
Published by: Нов български университет
Keywords: two-weight codes; strongly regular graphs; homogeneous weight; finite chain rings; linear codes; projective Hjelmslev geometries;

Summary/Abstract: It has been proved by Byrne, Greferath and Honold that a linear code over a finite Frobenius ring having exactly two homogeneous weights gives rise to a strongly regular graph. Up to now, only three infinite families of such codes are known. In this paper, we construct a new family of (homogeneous) two-weight linear codes over arbitrary chain rings of nilpotency index 2. These codes are defined geometrically as sets of points in certain projective Hjelmslev geometries. They provide a new example of an infinite class of two-weight codes over finite chain rings and produce an infinite family of strongly regular graphs.

  • Issue Year: 5/2009
  • Issue No: 1
  • Page Range: 83-88
  • Page Count: 6
  • Language: English