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
On completely regular binary codes and t-designs∗
✍ Scribed by J. Borges; J. Rifá; V.A. Zinoviev
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 283 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1571-0653
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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
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.
obtain a new for the of a -(u, A) design the block intersection st, sZ, . . , s, satisfy sr -sZ-. . . = s, = s(mod 2). This condition eliminates quasi-symmetric 2 -(20,10,18) and 2 -(60,30,58) designs. Quasi-symmetric 2 -(20,8,14) designs are eliminated by an ad hoc coding theoretic argument. A 2 -