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 …

Association schemes were originally introduced by Bose and his co-workers in the design of
statistical experiments. Since that point of inception, the concept has proved useful in the …

This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

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 …

This survey is mainly intended for non-specialists, though we try to include many recent
developments that may interest the experts as well. We want to study “good” finite subsets of …

We give a survey on various design theories from the viewpoint of algebraic combinatorics.
We will start with the following themes.(i) The similarity between spherical t-designs and …

Abstract Let F={0, 1, 2, 3} and define the set K={K 0, K 1, K 2} of relations on F such that (x,
y)∈ K i if and only if x− y≡±i (mod 4). Let n be a positive integer. We consider the Lee …

We study $ Q $-polynomial distance-regular graphs from the point of view of what we call
descendents, that is to say, those vertex subsets with the property that the width $ w $ and …

Motivated by the similarities between the theory of spherical $ t $-designs and that of $ t $-
designs in $ Q $-polynomial association schemes, we study two versions of relative $ t …

Linear programming bounds belong to the most powerful and flexible methods to obtain
bounds for extremal problems in coding theory as described in Chapter 12. Initially, Delsarte …