Abstract
The following problem motivated by investigation of databases is studied. Let \( \mathcal{C} \) be a q-ary code of length n with the properties that \( \mathcal{C} \) has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.
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Katona, G.O.H., Sali, A. & Schewe, KD. Codes that attain minimum distance in every possible direction. centr.eur.j.math. 6, 1–11 (2008). https://doi.org/10.2478/s11533-008-0001-4
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DOI: https://doi.org/10.2478/s11533-008-0001-4