Information on Result #689591
Linear OA(982, 6571, F9, 23) (dual of [6571, 6489, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(981, 6562, F9, 23) (dual of [6562, 6481, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(973, 6562, F9, 21) (dual of [6562, 6489, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(983, 6572, F9, 23) (dual of [6572, 6489, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(982, 5189, F9, 2, 23) (dual of [(5189, 2), 10296, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(982, 5189, F9, 3, 23) (dual of [(5189, 3), 15485, 24]-NRT-code) | [i] | ||
| 4 | Digital (59, 82, 5189)-net over F9 | [i] | ||
| 5 | Linear OOA(982, 3285, F9, 2, 23) (dual of [(3285, 2), 6488, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(982, 2190, F9, 3, 23) (dual of [(2190, 3), 6488, 24]-NRT-code) | [i] | ||