A Diametric Theorem in ${\mathbb Z}^n_m$ for Lee and Related Distances

  • Authors:

  • Rudolf Ahlswede;Faina I. Solov'Eva

  • Affiliations:

  • Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany 33501;Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia 630090

  • Venue:
  • ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
  • Year:
  • 2008

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Abstract

We present the diametric theorem for additive anticodes with respect to the Lee distance in ${\mathbb Z}^n_{2^k}$, where ${\mathbb Z}_{2^k}$ is an additive cyclic group of order 2k. We also investigate optimal anticodes in ${\mathbb Z}^n_{p^k}$ for the homogeneous distance and in ${\mathbb Z}^n_m$ for the Krotov-type distance.