Description
A block code that encodes \(K\) states (codewords) into an alphabet whose coordinates are elements of the dihedral group.Notes
Dihedral codes may be relevant to computation over MAC [6].Member of code lists
Primary Hierarchy
Parents
Dihedral codes are group-alphabet codes for the dihedral group \(G=D_n\).
Dihedral code
References
- [1]
- J. Verhoeff, “Error detecting decimal codes”, (1969)
- [2]
- H. Gumm, “A new class of check-digit methods for arbitrary number systems (Corresp.)”, IEEE Transactions on Information Theory 31, 102 (1985) DOI
- [3]
- A. Barg, “At the Dawn of the Theory of Codes”, The Mathematical Intelligencer 15, 20 (1993) DOI
- [4]
- J. A. Gallian, “The Mathematics of Identification Numbers”, The College Mathematics Journal 22, 194 (1991) DOI
- [5]
- K. Conrad, “Dihedral groups”, Lecture notes (2017)
- [6]
- A. G. Sahebi and S. S. Pradhan, “Codes over non-Abelian groups: Point-to-point communications and computation over MAC”, 2012 IEEE International Symposium on Information Theory Proceedings 631 (2012) DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-11-09)
- Alexander Barg (2025-11-09)
Cite as:
“Dihedral code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/dihedral, arXiv:2606.11484