J. Goethals

Publications46
h-index25
Citations3,119
Highly Influential Citations293
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Spherical codes and designs
Publisher Summary This chapter provides an overview of spherical codes and designs. A finite non-empty set X of unit vectors in Euclidean space R d has several characteristics, such as the dimension… Expand
SPHERICAL CODES AND DESIGNS
Publisher Summary This chapter provides an overview of spherical codes and designs. A finite non-empty set X of unit vectors in Euclidean space R d has several characteristics, such as the dimension… Expand
BOUNDS FOR SYSTEMS OF LINES, AND JACOBI POLYNOMIALS
Bounds are obtained for the cardinality of sets of lines having a prescribed number of angles, both in real and in complex Euclidean n-space. Extremal sets provide combinatorial configurations with a… Expand
On Generalized Reed-Muller Codes and Their Relatives
TLDR
The polynomial formulation of generalized ReedMuller codes is somewhat formalized and an extensive study is made of the interrelations between the m- variable approach of Kasami, Lin, and Peterson and the one-variable approach of Mattson and Solomon. Expand
Alternating Bilinear Forms over GF(q)
ORTHOGONAL MATRICES WITH ZERO DIAGONAL
1. Introduction. C-matrices appear in the literature at various places; for a survey, see [11]. Important for the construction of Hadamard matrices are the symmetric C-matrices, of order v = 2 (mod… Expand
Line graphs, root systems, and elliptic geometry
Publisher Summary The chapter discusses star-closed sets of lines at 60 ° and 90 ° , leading to a theorem that leaves only a restricted number of possibilities, of a specific structure. These… Expand
Strongly regular graphs derived from combinatorial designs
Publisher Summary This chapter explores strongly regular graphs derived from combinatorial designs. It presents graphs that are undirected, without loops, and without multiple edges. It discusses the… Expand
THREE-WEIGHT CODES AND ASSOCIATION SCHEMES
Three-weight projective codes C are considered for which the restrietion to C of the Hamming association scheme Hn(q) is an association scheme with three classes. Sufficient conditions are… Expand
Strongly Regular Graphs Having Strongly Regular Subconstituents
The chapter reviews the Bose–Mesner algebra of a strongly regular graph Γ , and presents in the i th eigenspace V i , i ∈ {1, 2} a special basis relative to some vertex of the graph. The Krein… Expand
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