Information on Result #689114
Linear OA(9146, 531455, F9, 27) (dual of [531455, 531309, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(9145, 531442, F9, 27) (dual of [531442, 531297, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(9133, 531442, F9, 25) (dual of [531442, 531309, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(9147, 531456, F9, 27) (dual of [531456, 531309, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9146, 435640, F9, 2, 27) (dual of [(435640, 2), 871134, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9146, 435640, F9, 3, 27) (dual of [(435640, 3), 1306774, 28]-NRT-code) | [i] | ||
| 4 | Digital (119, 146, 435640)-net over F9 | [i] | ||
| 5 | Linear OOA(9146, 265727, F9, 2, 27) (dual of [(265727, 2), 531308, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(9146, 177151, F9, 3, 27) (dual of [(177151, 3), 531307, 28]-NRT-code) | [i] | ||
| 7 | Linear OOA(9146, 40881, F9, 27, 27) (dual of [(40881, 27), 1103641, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |