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On Codes Correcting Symmetric Rank Errors

  • Nina I. Pilipchuk
  • Ernst M. Gabidulin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)

Abstract

We study the capability of rank codes to correct so-called symmetric errors beyond the \(\left\lfloor \frac{d-1}{2}\right\rfloor\) bound. If \(d\ge \frac{n+1}{2}\), then a code can correct symmetric errors up to the maximal possible rank \(\lfloor\frac{n-1}{2}\rfloor\). If \(d\le \frac{n}{2}\), then the error capacity depends on relations between d and n. If \((d+j)\nmid n,\;j=0,1,\dots,m-1\), for some m, but (d+m) | n, then a code can correct symmetric errors up to rank \(\lfloor\frac{d+m-1}{2}\rfloor\). In particular, one can choose codes correcting symmetric errors up to rank d–1, i.e., the error capacity for symmetric errors is about twice more than for general errors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nina I. Pilipchuk
    • 1
  • Ernst M. Gabidulin
    • 1
  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia

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