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JOURNAL OF
ALGEBRAIC
COMBINATORICS

  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Cyclotomy and Strongly Regular Graphs

A.E. Brouwer , R.M. Wilson and Qing Xiang

DOI: 10.1023/A:1018620002339

Abstract

We consider strongly regular graphs defined on a finite field by taking the union of some cyclotomic classes as difference set. Several new examples are found.

Pages: 25–28

Keywords: cyclotomy; Gauss sum; strongly regular graph

Full Text: PDF

References

R. Calderbank and W.M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18 (1986), 97-122. C.L.M. de Lange, Some new cyclotomic strongly regular graphs, J. Alg. Combin. 4 (1995), 329-330. J.H. van Lint and A. Schrijver, Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields, $Combinatorica 1$ (1981), 63-73. R.J. McEliece and H. Rumsey, Jr., Euler products, cyclotomy and coding, J. Number Th. 4 (1972), 302-311. R.J. McEliece, Irreducible cyclic codes and Gauss sums, in $Combinatorics$, pp. 183-200 ( Proc. NATO Advanced Study Inst., Breukelen, 1974; M. Hall, Jr. and J. H. van Lint (Eds.)), Part 1, Math. Centre Tracts, Vol. 55, Math. Centrum, Amsterdam,
1974. Republished by Reidel, Dordrecht, 1975 (pp. 185-202). R.M. Wilson and Qing Xiang, Cyclotomy, half ovoids and two-weight codes, Unpublished preprint, 1997.




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