Information on Result #689269
Linear OA(9122, 59061, F9, 27) (dual of [59061, 58939, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(9121, 59050, F9, 27) (dual of [59050, 58929, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(9111, 59050, F9, 25) (dual of [59050, 58939, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 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(9123, 59062, F9, 27) (dual of [59062, 58939, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9122, 52838, F9, 2, 27) (dual of [(52838, 2), 105554, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9122, 52838, F9, 3, 27) (dual of [(52838, 3), 158392, 28]-NRT-code) | [i] | ||
| 4 | Digital (95, 122, 52838)-net over F9 | [i] | ||
| 5 | Linear OOA(9122, 29530, F9, 2, 27) (dual of [(29530, 2), 58938, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(9122, 19687, F9, 3, 27) (dual of [(19687, 3), 58939, 28]-NRT-code) | [i] | ||
| 7 | Linear OOA(9122, 4543, F9, 27, 27) (dual of [(4543, 27), 122539, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |