The approach of Kalai and Kahn towards counterexamples of Borsuk's conjecture is
generalized to spherical codes. This allows the construction of a finite set in R 323 which …

In this paper we show that there is essentially only one way of arranging 240 (resp. 196560)
nonoverlapping unit spheres in R8 (resp. R24) so that they all touch another unit sphere …

We investigate the possibilities for attaining two Levenshtein upper bounds for spherical
codes. We find the distance distributions of all codes meeting these bounds. Then we show …

We use techniques of Bannai and Sloane to give a new proof that there is a unique (22,891,
1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a …

We consider spherical codes attaining the Levenshtein upper bounds on the cardinality of
codes with prescribed maximal inner product. We prove that the even Levenshtein bounds …

We investigate perfect codes in Z n in the ℓ p metric. Upper bounds for the packing radius r
of a linear perfect code, in terms of the metric parameter p and the dimension n are derived …

We consider bounds on codes in spherical caps and related problems in geometry and
coding theory. An extension of the Delsarte method is presented that relates upper bounds …

We are going to apply some simple algebraic geometry and number theory to codes and
sphere packings. These constructions look rather exciting since on the one hand they lead …

We prove that the kissing number in 48 dimensions among antipodal spherical codes with
certain forbidden inner products is 52 416 000. Constructions of attaining codes as kissing …

In [4] is given an inductive proof of the existence of families of orphans of RM (1, m) whose
weight distributions are {2 m− 1−∈ 2 (m+ k− 2)/2|∈=− 1, 0, 1}, where k satisfies 0≤ k< m …