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On Lower Bounds For Covering Codes

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Abstract

We study lower bounds on K(n,R), the minimum number of codewords of any binary code of length n such that the Hamming spheres of radius R with center at codewords cover the Hamming space \(\mathbb{F}_(\text(2))n \). We generalize Honkala's idea toobtain further improvements only by using some simple observationsof Zhang's result. This leads to nineteen improvements of thelower bound on K(n,R) within the range of \(1 \leqslant n \leqslant {\text{33, 1}} \leqslant R \leqslant {\text{10}}\).

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kanpur, INDIA–, 208 016

    M. C. Bhandari, K. K. P. Chanduka & A. K. Lal

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  1. M. C. Bhandari
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  2. K. K. P. Chanduka
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  3. A. K. Lal
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Bhandari, M.C., Chanduka, K.K.P. & Lal, A.K. On Lower Bounds For Covering Codes. Designs, Codes and Cryptography 15, 237–243 (1998). https://doi.org/10.1023/A:1008364924033

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