A characterization of codes meeting the Griesmer bound
✍ Scribed by Tor Helleseth
- Book ID
- 114037550
- Publisher
- Elsevier Science
- Year
- 1981
- Weight
- 998 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0019-9958
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We investigate codes meeting the Griesmer bound. The main theorem of this article is the generalization of the nonexistence theorem of Maruta (Des. Codes Cryptography 12 (1997) 83-87) to a larger class of codes.
## Helleseth, T., Projective codes meeting the Griesmer bound, Discrete Mathematics 106/107 (1992) 265-271. We present a brief survey of projective codes meeting the Griesmer bound. Methods for constructing large families of codes as well as sporadic codes meeting the bound are given. Current res
For any In, k, d; q]-code the Griesmer bound says that n >t ~ F d/q' 7. The purpose of this paper is to characterize all In, k, qk-1 \_ 3q~; q]-codes meeting the Griesmer bound in the case where k >/3, q >~ 5 and 1 ~</~ < k -1. It is shown that all such codes have a generator matrix whose columns co
We prove that if a linear code over GF( p), p a prime, meets the Griesmer bound, then if p e divides the minimum weight, p e divides all word weights. We present some illustrative applications of this result.