Packing radius, covering radius, and dual distance

摘要

Tietaivainen (1991) derived an upper bound on the covering radiusof codes as a function of the dual distance. This was generalized to theminimum distance, and to Q-polynomial association schemes by Levenshteinand Fazekas. Both proofs use a linear programming approach. Inparticular, Levenshtein and Fazekas (1990) use linear programming boundsfor codes and designs. In this article, proofs relying solely on theorthogonality relations of Krawtchouk (1929), Lloyd, and, moregenerally, Krawtchouk-adjacent orthogonal polynomials are derived. As aby-product upper bounds on the minimum distance of formally self-dualbinary codes are derived