Information on Result #1303360
Linear OA(999, 1062890, F9, 17) (dual of [1062890, 1062791, 18]-code), using construction X with Varšamov bound based on
- linear OA(998, 1062888, F9, 17) (dual of [1062888, 1062790, 18]-code), using
- trace code [i] based on linear OA(8149, 531444, F81, 17) (dual of [531444, 531395, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(8149, 531441, F81, 17) (dual of [531441, 531392, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(8149, 531444, F81, 17) (dual of [531444, 531395, 18]-code), using
- linear OA(998, 1062889, F9, 16) (dual of [1062889, 1062791, 17]-code), using Gilbert–Varšamov bound and bm = 998 > Vbs−1(k−1) = 67 161535 276655 786466 344306 903810 165602 895649 648641 161935 720534 620423 756743 127585 718948 043329 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 OOA(999, 1062890, F9, 2, 17) (dual of [(1062890, 2), 2125681, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(999, 1062890, F9, 3, 17) (dual of [(1062890, 3), 3188571, 18]-NRT-code) | [i] | ||
| 3 | Digital (82, 99, 1062890)-net over F9 | [i] | ||
| 4 | Linear OOA(999, 531445, F9, 2, 17) (dual of [(531445, 2), 1062791, 18]-NRT-code) | [i] | OOA Folding | |