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.

Constructions of linear codes with small hulls from association schemes

“…Three-class association scheme is an important type of association scheme. In [11], the authors give some constructions of symmetric three-class association schemes as the fusion schemes of the cyclotomic association schemes. Now we will employ one of these three-class association schemes to construct LCD codes and linear codes with one-dimensional hull by Theorem 3.4.…”

“…The first eigenmatrix of this case is given by Eq. (11). Let C be a linear code over F p u 0 with generator matrix [I q , Q 1 , Q 2 ], where Q 1 = 2A 0 + A 1 +6A 2 +4A 3 , Q 2 = A 0 +3A 1 +5A 2 +4A 3 .…”

Three-valued Gauss periods, circulant weighing matrices and association schemes

“…Let Then |S| = p f + 1, and g F,N = p f S − Z N . As in [9], we identify the points of the projective plane P G(2, p f ) with the elements of Z N . Then S represents a line of P G(2, p f ), and is the well-known Singer difference set in Z N ; see [13] for instance.…”

“…Note that with the same notation as above, in the special case where p = 2, the authors of [9] already showed that the Cayley graph Cay(F q , C (N,q) 0 ), with q = 2 6f and N = (2 3f − 1)/(2 f − 1), has three restricted eigenvalues . This can be seen as follows.…”