Weight distribution and dual distance |
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Authors: | Patrick Solé |
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Affiliation: | (1) Laboratoire I.3.S., CNRS-URA 1376, Bâtiment 4, 250 rue Albert Einstein, Sophia-Antipolis, F-06560 Valbonne, France |
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Abstract: | Several results in coding theory (e.g. the Carlitz-Uchiyama bound) show that the weight distributions of certain algebraic codes of lengthn are concentrated aroundn/2 within a range of width n. It is proved in this article that the extreme weights of a linear binary code of sufficiently high dual distance cannot be too close ton/2, the gap being of order n. The tools used involve the Pless identities and the orthogonality properties of Krawtchouk polynomials, as well as estimates on their zeroes. As a by-product upper bounds on the minimum distance of self-dual binary codes are derived. |
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Keywords: | Orthogonal Polynomials Krawtchouk Polynomials Coding Theory Pless Identities Dual Distance Self-dual Codes |
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