Neumaier, A., Completely regular codes, Discrete Mathematics 106/107 (1992) 353-360 Completely regular codes are a large class of codes which share many of the most interesting properties of perfect codes. This paper shows that the basic theory-including Lloyd's theorem+an be obtained very elegantly
A note on completely regular codes
โ Scribed by A.E. Brouwer
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 169 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
We show that puncturing a completely regular even binary code produces a completely regular code again, thus answering a question posed in Brouwer et al. [3], p. 357.
๐ SIMILAR VOLUMES
A binary code C is said to be completely regular if the weight distribution of any translate x + C depends only on the distance of x to C. Such codes are related to designs and distance regular graphs. Their covering radius is equal to their external distance. All perfect and uniformly packed codes
Courteau, B. and A. Montpetit, Dual distances of completely regular codes, Discrete Mathematics 89 (1991) 7-15. In this paper we prove two theorems giving arithmetical constraints on the possible values of dual distances of completely regular codes extending some recent results of Calderbank and Gce
In their paper (J. Combin. Theory Ser. A 64 (1993), 10 30) Brualdi and Pless prove linearity of some binary codes obtained by a greedy algorithm and establish lower bounds for the dimension of these codes. In this note, we show that actually they have proved a much more general result, and show that