Minimal coverings of {0,1,2}n with spheres of radius n

Authors

  • Kolev, Emil
  • Baicheva, Tsonka

Abstract

Consider the set Qn = {0,1,2}n equipped with the usual Hamming distance. Denote by T(n) the minimal number of spheres of radius n needed to cover Qn- The exact values of T(n) are known for n ≤ 8. The first undecided case is n = 9 and it is known that 67 ≤ T(9) ≤ 68. We settle the case by showing that T(9) = 68. The inequality T(9) = 68 implies T( 10) ≥ 102, T(11) ≥ 153, T(12) ≥ 230 and T(13) ≥ 345 thus improving the best known lower bounds for 10 ≤ n ≤ 13. © 2015 Utilitas Mathematics.

Published

2017-06-09

How to Cite

Kolev, Emil, & Baicheva, Tsonka. (2017). Minimal coverings of {0,1,2}n with spheres of radius n. Utilitas Mathematica, 103. Retrieved from https://utilitasmathematica.com/index.php/Index/article/view/1221

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