Algebraic combinatorics is the study of combinatorial objects as an extension of the study of
finite permutation groups, or, in other words, group theory without groups. In the spirit of …

Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

In this article we investigate the N-point min-max and max-min polarization problems on the
sphere for a large class of potentials in R n. We derive universal lower and upper bounds on …

This article is devoted to the study of discrete potentials on the sphere in Rn for sharp codes.
We show that the potentials of most of the known sharp codes attain the universal lower …

In this paper, we first provide an inductive construction of designs on compact groups G from
those on subgroups K when (G, K) is a Gelfand pair. We then use the construction to provide …

Unitary t-designs are'good'finite subsets of the unitary group that approximate the whole
unitary group well. Unitary t-designs have been applied in randomized benchmarking …

In this article we present a unified treatment for obtaining bounds on the potential energy of
codes in the general context of polynomial metric spaces (PM-spaces). The lower bounds …

Abstract Nebe, Rains and Sloane studied the polynomial invariants for real and complex
Clifford groups and they give a new conceptual proof that these invariants are spanned by …

We derive universal lower and upper bounds for max-min and min-max problems (also
known as polarization) for the potential of spherical $(k, k) $-designs and provide certain …

Relative $ t $-designs in the $ n $-dimensional hypercube $\mathcal {Q} _n $ are equivalent
to weighted regular $ t $-wise balanced designs, which generalize combinatorial $ t $-$(n …