Information on Result #689117
Linear OA(9110, 531455, F9, 21) (dual of [531455, 531345, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(9109, 531442, F9, 21) (dual of [531442, 531333, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(997, 531442, F9, 19) (dual of [531442, 531345, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(91, 13, F9, 1) (dual of [13, 12, 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(9111, 531456, F9, 21) (dual of [531456, 531345, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(9112, 531457, F9, 21) (dual of [531457, 531345, 22]-code) | [i] | ||
| 3 | Linear OOA(9110, 295426, F9, 2, 21) (dual of [(295426, 2), 590742, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(9110, 295426, F9, 3, 21) (dual of [(295426, 3), 886168, 22]-NRT-code) | [i] | ||
| 5 | Digital (89, 110, 295426)-net over F9 | [i] | ||
| 6 | Linear OA(9112, 531458, F9, 21) (dual of [531458, 531346, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(9110, 265727, F9, 2, 21) (dual of [(265727, 2), 531344, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(9110, 177151, F9, 3, 21) (dual of [(177151, 3), 531343, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(9110, 53145, F9, 21, 21) (dual of [(53145, 21), 1115935, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |