Information on Result #1303314
Linear OA(987, 1062890, F9, 15) (dual of [1062890, 1062803, 16]-code), using construction X with Varšamov bound based on
- linear OA(986, 1062888, F9, 15) (dual of [1062888, 1062802, 16]-code), using
- trace code [i] based on linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8140, 531441, F81, 14) (dual of [531441, 531401, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(14) ⊂ Ce(13) [i] based on
- trace code [i] based on linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
- linear OA(986, 1062889, F9, 14) (dual of [1062889, 1062803, 15]-code), using Gilbert–Varšamov bound and bm = 986 > Vbs−1(k−1) = 195 072413 999866 799737 070240 225918 780898 980107 649052 852020 357181 796822 988194 814529 [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(987, 1062890, F9, 2, 15) (dual of [(1062890, 2), 2125693, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(987, 1062890, F9, 3, 15) (dual of [(1062890, 3), 3188583, 16]-NRT-code) | [i] | ||
| 3 | Digital (72, 87, 1062890)-net over F9 | [i] | ||
| 4 | Linear OOA(987, 531445, F9, 2, 15) (dual of [(531445, 2), 1062803, 16]-NRT-code) | [i] | OOA Folding | |