A Combinatorial construction of the Gray map over Galois rings

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6 Scopus citations


In this correspondence, we will introduce a new combinatorial method for a coordinate-wise construction of the homogeneous-weight preserving Gray map for Galois rings by using elementary tools from Affine Geometries. Our construction differs in the methods used from the algebraic constructions done previously in [M. Greferath, S.E. Schmidt, Gray Isometries for finite chain rings and a nonlinear ternary (36, 312, 15) code, IEEE Trans. Inform. Theory 45 (1999) 2522-2524; S. Ling, J.T. Blackford, Zp k + 1-linear codes, IEEE Trans. Inform. Theory 48 (2002) 2592-2605].

Original languageEnglish (US)
Pages (from-to)3408-3412
Number of pages5
JournalDiscrete Mathematics
Issue number10
StatePublished - May 28 2009
Externally publishedYes


  • Affine Geometries
  • Affine Hyperplanes
  • Galois rings
  • Gray maps
  • Homogenous weights
  • Linear codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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