✦ LIBER ✦
Quasi-Symmetric Designs and Codes Meeting the Grey–Rankin Bound
✍ Scribed by Gary McGuire
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 261 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
We give a characterization of codes meeting the Grey Rankin bound. When the codes have even length, the existence of such codes is equivalent to the existence of certain quasi-symmetric designs. We also find the parameters of all linear codes meeting the Grey Rankin bound.
1997 Academic Press
Theorem A. Suppose n and d satisfy n&-n<2d<n. Then:
(i) If n is odd, there exists a self-complementary code meeting the Grey Rankin bound if and only if there exists a Hadamard matrix of size n+1.