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.
On the nonexistence of some quaternary linear codes meeting the Griesmer bound
β Scribed by Noboru Hamada
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 176 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
β¦ Synopsis
It is unknown whether or not there exists a quaternary linear code with parameters [293, 5, 219], [289, 5, 216] or [277, 5, 207]. The purpose of this paper is to prove the nonexistence of quaternary linear codes with parameters [
π SIMILAR VOLUMES
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.
In this paper we prove the nonexistence of quaternary linear codes with parameters [51,4, 37]. This result gives the exact value of n q (k, d) for q Ο 4, k Ο 4, d Ο 37 and 38. These were the only minimum distances for which the optimal length of a four-dimensional quaternary code was unknown. The pr