Information on Result #675343
Linear OA(382, 6580, F3, 15) (dual of [6580, 6498, 16]-code), using construction X4 applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(381, 6562, F3, 15) (dual of [6562, 6481, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(365, 6562, F3, 13) (dual of [6562, 6497, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(317, 18, F3, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,3)), using
- dual of repetition code with length 18 [i]
- linear OA(31, 18, F3, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(383, 6581, F3, 15) (dual of [6581, 6498, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(384, 6582, F3, 15) (dual of [6582, 6498, 16]-code) | [i] | ||
| 3 | Linear OA(385, 6583, F3, 15) (dual of [6583, 6498, 16]-code) | [i] | ||
| 4 | Linear OA(385, 6584, F3, 15) (dual of [6584, 6499, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(386, 6586, F3, 15) (dual of [6586, 6500, 16]-code) | [i] | ||
| 6 | Linear OOA(382, 3290, F3, 2, 15) (dual of [(3290, 2), 6498, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(382, 1645, F3, 4, 15) (dual of [(1645, 4), 6498, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(382, 1316, F3, 5, 15) (dual of [(1316, 5), 6498, 16]-NRT-code) | [i] | ||