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doi: 10.1109/18.370102
Recently, A. Tietäväinen 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 Levenshtein and Fazakas. Both proofs use a linear programming approach. In this correspondence the author rederives in a simple way known upper bounds on the minimum distance and covering radius of a \(q\)-ary unrestricted code with the zero codeword when the dual distance is known. The main idea is to interpret the Pless identities as equalities between two scalar products on vector spaces of polynomials: those associated with the weight distribution and those associated with the binomial distribution. As a by-product upper bounds on the minimum distance of formally self- dual binary codes are derived.
Bounds on codes, upper bounds, covering radius, \(q\)-ary unrestricted code, Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory, minimum distance, self-dual binary codes
Bounds on codes, upper bounds, covering radius, \(q\)-ary unrestricted code, Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory, minimum distance, self-dual binary codes
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