PACKING RADIUS, COVERING RADIUS, AND DUAL DISTANCE

Recently, A Tietaivainen derived an upper bound on the covering radius of codes as a function of the dual distance. This was generalized to the minimum distance, and to Q-polynomial association schemes by Leven shtein and Fazekas. Both proofs use a linear programming approach. In particular, Levenshtein and Fazekas use linear programming bounds for codes and designs. In this correspondence, proofs relying solely on th e orthogonality relations of Krawtchouk, Lloyd, and, more generally, K rawtchouk-adjacent orthogonal polynomials are derived. As a by-product upper bounds on the minimum distance of formally self-dual binary cod es are derived.