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Strongly regular graphs from weakly regular plateaued functions
The paper provides the first constructions of strongly regular graphs and
association schemes from weakly regular plateaued functions over finite fields
of odd characteristic. We generalize the construction method of strongly
regular graphs from weakly regular bent functions given by Chee et al. in
[Journal of Algebraic Combinatorics, 34(2), 251-266, 2011] to weakly regular
plateaued functions. In this framework, we construct strongly regular graphs
with three types of parameters from weakly regular plateaued functions with
some homogeneous conditions. We also construct a family of association schemes
of class p from weakly regular p-ary plateaued functions
Strongly Regular Graphs Constructed from -ary Bent Functions
In this paper, we generalize the construction of strongly regular graphs in
[Y. Tan et al., Strongly regular graphs associated with ternary bent functions,
J. Combin.Theory Ser. A (2010), 117, 668-682] from ternary bent functions to
-ary bent functions, where is an odd prime. We obtain strongly regular
graphs with three types of parameters. Using certain non-quadratic -ary bent
functions, our constructions can give rise to new strongly regular graphs for
small parameters.Comment: to appear in Journal of Algebraic Combinatoric
Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which
is conjectured to be a universally optimal code. We show that this scheme has a
generalization in terms of Kerdock codes, as well as in terms of maximal real
mutually unbiased bases. These schemes also related to extremal line-sets in
Euclidean spaces and Barnes-Wall lattices. D. de Caen and E. R. van Dam
constructed two infinite series of formally dual 3-class association schemes.
We explain this formal duality by constructing two dual abelian schemes related
to quaternary linear Kerdock and Preparata codes.Comment: 16 page
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