On the minimum size of binary codes with length 2R + 4 and covering radius R

  • Authors:

  • Gerzson Kéri;Patric R. Östergård

  • Affiliations:

  • Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary 1111;Department of Electrical and Communications Engineering, Helsinki University of Technology, TKK, Finland 02015

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2008

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Abstract

The minimum size of a binary code with length n and covering radius R is denoted by K(n, R). For arbitrary R, the value of K(n, R) is known when n 驴 2R + 3, and the corresponding optimal codes have been classified up to equivalence. By combining combinatorial and computational methods, several results for the first open case, K(2R + 4, R), are here obtained, including a proof that K(10, 3) = 12 with 11481 inequivalent optimal codes and a proof that if K(2R + 4, R) R then this inequality cannot be established by the existence of a corresponding self-complementary code.