G. Fazekas et Vi. Levenshtein, ON UPPER-BOUNDS FOR CODE DISTANCE AND COVERING RADIUS OF DESIGNS IN POLYNOMIAL METRIC-SPACES, J COMB TH A, 70(2), 1995, pp. 267-288
The purpose of this paper is to present new upper bounds for code dist
ance and covering radius of designs in arbitrary polynomial metric spa
ces. These bounds and the necessary and sufficient conditions of their
attainability were obtained as the solution of an extremal problem fo
r systems of orthogonal polynomials. For antipodal spaces the behaviou
r of the bounds in different asymptotical processes is determined and
it is proved that this bound is attained for all tight 2k-design. (C)
1995 Academic Press, Inc.