Completely regular code[1]
Description
A code \(C\) is completely regular if the weight distribution of any coset \(e+C\) depends only on the distance \(d(e,C)\) of \(e\) to \(C\) [2].
Notes
See review [2] on completely regular codes.
Parent
Children
- Perfect code — Perfect codes and extended perfect codes are completely regular [2].
- Uniformly packed code — Uniformly packed codes are completely regular [3][2; Prop. 2.6].
References
- [1]
- Delsarte, Philippe. "An algebraic approach to the association schemes of coding theory." Philips Res. Rep. Suppl. 10 (1973)
- [2]
- J. Borges, J. Rifà, and V. A. Zinoviev, “On Completely Regular Codes”, (2017) arXiv:1703.08684
- [3]
- J. M. Goethals and H. C. A. Van Tilborg. “Uniformly packed codes”. In Philips Research Reports 30.1 (1975)
Page edit log
- Victor V. Albert (2024-08-16) — most recent
Cite as:
“Completely regular code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/completely_regular