Information on Result #689578
Linear OA(9138, 6571, F9, 39) (dual of [6571, 6433, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,18]) based on
- linear OA(9137, 6562, F9, 39) (dual of [6562, 6425, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(9129, 6562, F9, 37) (dual of [6562, 6433, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 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(9139, 6572, F9, 39) (dual of [6572, 6433, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(9140, 6573, F9, 39) (dual of [6573, 6433, 40]-code) | [i] | ||
| 3 | Linear OOA(9138, 6231, F9, 2, 39) (dual of [(6231, 2), 12324, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(9138, 6231, F9, 3, 39) (dual of [(6231, 3), 18555, 40]-NRT-code) | [i] | ||
| 5 | Digital (99, 138, 6231)-net over F9 | [i] | ||
| 6 | Linear OA(9139, 6573, F9, 39) (dual of [6573, 6434, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(9140, 6575, F9, 39) (dual of [6575, 6435, 40]-code) | [i] | ||
| 8 | Linear OOA(9138, 3285, F9, 2, 39) (dual of [(3285, 2), 6432, 40]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(9138, 2190, F9, 3, 39) (dual of [(2190, 3), 6432, 40]-NRT-code) | [i] | ||