Three-class association schemes from cyclotomy

Abstract We give three constructions of three-class association schemes as fusion schemes of the cyclotomic scheme, two of which are primitive.

[1]  Tao Feng,et al.  Constructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes , 2012, Comb..

[2]  Dieter Jungnickel,et al.  The Solution of the Waterloo Problem , 1995, J. Comb. Theory, Ser. A.

[3]  E. V. Dam.  Three-Class Association Schemes , 1999 .

[4]  Bernhard Schmidt,et al.  All Two-Weight Irreducible Cyclic Codes? , 2002 .

[5]  A. Munemasa,et al.  Davenport-Hasse theorem and cyclotomic association schemes , 2006 .

[6]  J. Koolen,et al.  Distance-regular graphs , 2014, 1410.6294.

[7]  Cunsheng Ding,et al.  A family of skew Hadamard difference sets , 2006, J. Comb. Theory, Ser. A.

[8]  Richard A. Games.  The geometry of quadrics and correlations of sequences , 1986, IEEE Trans. Inf. Theory.

[9]  K. Williams,et al.  Gauss and Jacobi sums , 2021, Mathematical Surveys and Monographs.

[10]  Eiichi Bannai,et al.  Subschemes of some association schemes , 1991 .

[11]  Tao Feng,et al.  Paley type group schemes from cyclotomic classes and Arasu-Dillon-Player difference sets , 2012 .

[12]  Koji Momihara,et al.  Strongly regular Cayley graphs, skew Hadamard difference sets, and rationality of relative Gauss sums , 2012, Eur. J. Comb..

[13]  Tao Feng,et al.  Cyclotomic constructions of skew Hadamard difference sets , 2011, J. Comb. Theory, Ser. A.

[14]  P. Delsarte.  AN ALGEBRAIC APPROACH TO THE ASSOCIATION SCHEMES OF CODING THEORY , 2011 .

[15]  Rudolf Lide,et al.  Finite fields , 1983 .

[16]  R. Calderbank,et al.  The Geometry of Two‐Weight Codes , 1986 .

[17]  Koji Momihara,et al.  Skew Hadamard Difference Sets from Cyclotomic Strongly Regular Graphs , 2012, SIAM J. Discret. Math..

[18]  Mikhail Muzychuk.  Skew Hadamard Difference Sets , 2010 .

[19]  E. Bannai,et al.  Algebraic Combinatorics I: Association Schemes , 1984 .

[20]  Akihiro Munemasa,et al.  Pseudocyclic association schemes and strongly regular graphs , 2008, Eur. J. Comb..

[21]  Koji Momihara,et al.  Lifting constructions of strongly regular Cayley graphs , 2014, Finite Fields Their Appl..

[22]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[23]  Tao Feng,et al.  Strongly regular graphs from unions of cyclotomic classes , 2010, J. Comb. Theory, Ser. B.

[24]  Hanfried Lenz,et al.  Design theory , 1985 .

[25]  Gennian Ge,et al.  Constructions of strongly regular Cayley graphs using index four Gauss sums , 2012, 1201.0702.

[26]  A. Hora,et al.  Distance-Regular Graphs , 2007 .

[27]  E. R. van Dam,et al.  Regular graphs with four eigenvalues , 1995 .

[28]  Henk D. L. Hollmann,et al.  Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets , 1999, J. Comb. Theory, Ser. A.