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 ฯญ 4, k ฯญ 4, d ฯญ 37 and 38. These were the only minimum distances for which the optimal length of a four-dimensional quaternary code was unknown. The pr
The nonexistence of ternary [79,6,51] codes
โ Scribed by Noboru Hamada; Yoko Watamori
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 143 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
โฆ Synopsis
It is known (cf. Hamada, J. Combin. Inform. System Sci. 18 (1993b) that there is no ternary [78,6,51] code meeting the Griesmer bound and n 3(6; 51) = 79 or 80, where n3(k; d) denotes the smallest value of n for which there exists a ternary [n; k; d] code.
๐ SIMILAR VOLUMES
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 [
The code over a finite field F, of a design D is the space spanned by the incidence vectors of the blocks. It is shown here that if D is a Steiner triple system on v points, and if the integer then the ternary code C of contains a subcode that can be shortened to the ternary generalized Reed-Muller