Showing papers by "Richard A. Brualdi published in 1989"
TL;DR: The authors introduce a new function l(m,r), called the length function, which equals the smallest length of a binary code of codimension m and covering radius r, and investigates basic properties of thelength function.
Abstract: The covering radius r of a code is the maximum distance from any vector in the space containing the code to the nearest codeword. The authors introduce a new function l(m,r), called the length function, which equals the smallest length of a binary code of codimension m and covering radius r. They investigate basic properties of the length function. Projective geometries over larger fields are used to construct families of codes which improve significantly the upper bound for l(m,2) obtained by amalgamation of Hamming codes. General methods are developed for ruling out the existence of codes of covering radius 2 with a given codimension and length resulting in lower bounds for l(m,2). A table is presented which gives the best results now known for l(m,r) with m >
62 citations
TL;DR: In this article, the authors studied the class of (0, 1, 2)-matrices with a prescribed row sum vector R and column sum vector S in the class U 2 (R,S).
3 citations
TL;DR: In this paper, the existence and structural properties of 2-multigraphs with a prescribed degree sequence were studied and they were defined to be parsimonious provided no 2multigraph with the same degree sequence has fewer edges in its supporting (i.e., underlying) graph.
Abstract: We study both existence and structural properties of 2-multigraphs in the class of all 2-multigraphs with a prescribed degree sequence D. A 2-multigraph in defined to be parsimonious provided no 2-multigraph with the same degree sequence has fewer edges in its supporting (i.e., underlying) graph. In a parsimonious 2-multigraph G each connected component of the graph Gr formed by the edges of multiplicity 1 is either a star or a triangle. We attempt to understand the relationship between degree sequences and these graphs Gr .
3 citations