# The Nonexistence of Ternary [284, 6, 188] Codes

The Nonexistence of Ternary [284, 6, 188] Codes Let [n, k, d] q codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). Let n q (k, d) be the smallest value of n for which there exists an [n, k, d] q code. It is known from [1, 2] that 284 ≤ n 3(6, 188) ≤ 285 and 285 ≤ n 3(6, 189) ≤ 286. In this paper, the nonexistence of [284, 6, 188]3 codes is proved, whence we get n 3(6, 188) = 285 and n 3(6, 189) = 286. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# The Nonexistence of Ternary [284, 6, 188] Codes

, Volume 40 (2) – Dec 16, 2004
12 pages

/lp/springer_journal/the-nonexistence-of-ternary-284-6-188-codes-446OXCE93Y
Publisher
Springer Journals
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/B:PRIT.0000043927.19508.8b
Publisher site
See Article on Publisher Site

### Abstract

Let [n, k, d] q codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). Let n q (k, d) be the smallest value of n for which there exists an [n, k, d] q code. It is known from [1, 2] that 284 ≤ n 3(6, 188) ≤ 285 and 285 ≤ n 3(6, 189) ≤ 286. In this paper, the nonexistence of [284, 6, 188]3 codes is proved, whence we get n 3(6, 188) = 285 and n 3(6, 189) = 286.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Dec 16, 2004

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