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

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.

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