Titlebook: Coding Theory and Design Theory; Part I Coding Theory Dijen Ray-Chaudhuri Conference proceedings 1990 Springer-Verlag New York, Inc. 1990 C

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Self-Dual Codes and Self-Dual Designs,We construct self-orthogonal binary codes from projective 2 - (., ., λ) designs with a polarity, . odd, and λ even. We give arithmetic conditions on the parameters of the design to obtain self-dual or doubly even self-dual codes. Non existence results in the latter case are obtained from rationality conditions of certain strongly regular graphs.

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,Some Recent Results on Signed Graphs with Least Eigenvalues ≥ -2,A survey of some results concerning the class of sigraphs represented by root-systems .., n ∈ . and .. is given and some unsolved problems are described.

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Coding Theory and Design Theory978-1-4613-8994-1Series ISSN 0940-6573 Series E-ISSN 2198-3224

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Steven Footitt,William E. Finch-Savagest a code of codimension 11 and covering radius 2 which has length 64. We conclude with a table which gives the best available information for the length of a code with codimension . and covering radius . for 2 ≤ . ≤ 24 and 2 ≤ . ≤ 24.

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Leónie Bentsink,Maarten Koornneefessary and sufficient condition is found to determine when a metric scheme admits a nontrivial perfect multiple covering. Results specific to the classical Hamming and Johnson schemes are given which bear out the relationship between .-designs, orthogonal arrays, and perfect multiple coverings.

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On the Length of Codes with a Given Covering Radius,st a code of codimension 11 and covering radius 2 which has length 64. We conclude with a table which gives the best available information for the length of a code with codimension . and covering radius . for 2 ≤ . ≤ 24 and 2 ≤ . ≤ 24.

Inertia

Perfect Multiple Coverings in Metric Schemes,essary and sufficient condition is found to determine when a metric scheme admits a nontrivial perfect multiple covering. Results specific to the classical Hamming and Johnson schemes are given which bear out the relationship between .-designs, orthogonal arrays, and perfect multiple coverings.

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