Distance regular covers of the complete graph (Q1204463)

A graph \(G\) is distance regular if for any two vertices \(u\) an \(v\) the number of vertices being at distance \(i\) from \(u\) and \(j\) from \(v\) depends on \(i\) and \(j\) only. \(G\) is called antipodal if the vertices at distance \(d\) from a given vertex are also at distance \(d\) from each other. Authors prove necessary existence conditions for distance regular antipodal graphs of diameter 3 in terms of three parameters assigned to each such graph, and give a new construction for such graphs generalising a known one by Thas and Somma. They also investigate the relationship of distance regular antipodal graphs to other fields like design and coding theory.