Some New Cyclotomic Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
A new class of two weight codes
FFA '95 Proceedings of the third international conference on Finite fields and applications
Cyclotomy and Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
A Characterization of Association Schemes from Affine Spaces
Designs, Codes and Cryptography
Strongly Regular Decompositions of the Complete Graph
Journal of Algebraic Combinatorics: An International Journal
Some implications on amorphic association schemes
Journal of Combinatorial Theory Series A
All Two-Weight Irreducible Cyclic Codes?
Finite Fields and Their Applications
Commutative association schemes
European Journal of Combinatorics
Cyclotomic constructions of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
Strongly regular graphs from unions of cyclotomic classes
Journal of Combinatorial Theory Series B
Cyclotomy, gauss sums, difference sets and strongly regular cayley graphs
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
European Journal of Combinatorics
Constructions of strongly regular Cayley graphs using index four Gauss sums
Journal of Algebraic Combinatorics: An International Journal
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Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated symmetric design is trivial. We present several non-amorphous examples, which are either cyclotomic association schemes, or their fusion schemes. Special properties of symmetric designs guarantee the existence of further fusions, and the two known non-amorphous association schemes of class 4 discovered by van Dam and by the authors, are recovered in this way. We also give another pseudocyclic non-amorphous association scheme of class 7 on GF(2^2^1), and a new pseudocyclic amorphous association scheme of class 5 on GF(2^1^2).