Published January 1, 2014 | Version v1
Journal article Open

An Improvement of the Gilbert-Varshamov Bound Over Nonprime Fields

  • 1. Sabanci Univ, TR-34956 Istanbul, Turkey
  • 2. Tech Univ Denmark, Dept Appl Math & Comp Sci, DK-2800 Lyngby, Denmark
  • 3. Inst Nacl Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

Description

The Gilbert-Varshamov bound guarantees the existence of families of codes over the finite field F-l with good asymptotic parameters. We show that this bound can be improved for all nonprime fields F-l with l >= 49, except possibly l = 125. We observe that the same improvement even holds within the class of transitive codes and within the class of self-orthogonal codes.

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