Abstract
We describe a new construction of distance regular covers of a complete graph K 2t q with fibres of size q2t-1, q a power of 2. When q=2, the construction coincides with the one found in [D. de Caen, R. Mathon, G.E. Moorhouse. J. Algeb. Combinatorics, Vol. 4 (1995) 317] and studied in [T. Bending, D. Fon-Der-Flaass, Elect. J. Combinatorics, Vol. 5 (1998) R34]. The construction uses, as one ingredient, an arbitrary symmetric Latin square of order q; so, for large q, it can produce many different covers.
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T. Bending D. Fon-Der-Flaass (1998) ArticleTitleCrooked functions, bent functions, and distance regular graphs Elect. J. Combinatorics 5 14
A.E. Brouwer, A.M. Cohen and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, 1989.
D. de Caen R. Mathon G.E. Moorhouse (1995) ArticleTitleA family of antipodal distance-regular graphs related to the classical Preparata codes J. Algebr. Combinatorics 4 317–327
C.D. Godsil, Covers of Complete Graphs. In: Progress in Algebraic Combinatorics, Adv. Stud. Pure Math., Vol. 24 (1996) pp. 137–163.
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Caen, D.D., Fon-Der-Flaass, D. Distance Regular Covers of Complete Graphs from Latin Squares. Des Codes Crypt 34, 149–153 (2005). https://doi.org/10.1007/s10623-004-4851-x
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DOI: https://doi.org/10.1007/s10623-004-4851-x