Type II codes over F2 + uF2

Steven T. Dougherty, Philippe Gaborit, Masaaki Harada, Patrick Sole

Research output: Contribution to journalArticlepeer-review

171 Citations (Scopus)


The alphabet F2 + uF2 is viewed here as a quotient of the Gaussian integers by the ideal (2). Self-dual F2 + uF2 codes with Lee weights a multiple of 4 are called Type II. They give even uniniodular Gaussian lattices by Construction A, while Type I codes yield uniniodular Gaussian lattices. Construction B makes it possible to realize the Leech lattice as a Gaussian lattice. There is a Gray map which maps Type II codes into Type II binary codes with a fixed point free involution in their automorphism group. Combinatorial constructions use weighing matrices and strongly regular graphs. Gleason-type theorems for the symmetrized weight enumerators of Type II codes are derived. All self-dual codes are classified for length up to 8. The shadow of Type I codes yields bounds on the highest minimum Hamming and Lee weights.

Original languageEnglish
Pages (from-to)32-45
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number1
Publication statusPublished - 1999


  • Automorphism groups
  • Codes over rings
  • Gray map
  • Lattices and shadows


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