✦ LIBER ✦

Completely regular codes

✍ Scribed by Arnold Neumaier

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 404 KB
Volume: 106-107
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90565-w

No coin nor oath required. For personal study only.

✦ Synopsis

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 by methods inspired from the theory of distance regular graphs. d(x, C) := min{d(x, y) ) y E C}, and the covering radius tc := yEy d(x, C

📜 SIMILAR VOLUMES

Completely regular codes and completely

Completely regular codes and completely transitive codes

✍ Patrick Solé 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 511 KB

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

Dual distances of completely regular cod

Dual distances of completely regular codes

✍ B. Courteau; A. Montpetit 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 467 KB

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

A note on completely regular codes

✍ A.E. Brouwer 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 169 KB

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.

On complete regularity of extended codes

✍ A.E. Brouwer 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 158 KB

Completely regular designs

✍ William J. Martin 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 215 KB

We study a class of t-designs which enjoy a high degree of regularity. These are the subsets of vertices of the Johnson graph which are completely regular, in the sense of Delsarte [Philips Res. Reports Suppl. 10 (1973)]. After setting up the basic theory, we describe the known completely regular de

Perfect Completely Regular Semigroups

✍ Howard Hamilton 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 459 KB