Information on Result #1303286
Linear OA(981, 1062890, F9, 14) (dual of [1062890, 1062809, 15]-code), using construction X with Varšamov bound based on
- linear OA(980, 1062888, F9, 14) (dual of [1062888, 1062808, 15]-code), using
- trace code [i] based on linear OA(8140, 531444, F81, 14) (dual of [531444, 531404, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 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(8137, 531441, F81, 13) (dual of [531441, 531404, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(8140, 531444, F81, 14) (dual of [531444, 531404, 15]-code), using
- linear OA(980, 1062889, F9, 13) (dual of [1062889, 1062809, 14]-code), using Gilbert–Varšamov bound and bm = 980 > Vbs−1(k−1) = 298 240467 814920 615504 972458 445304 659306 778106 921731 579407 574850 312241 650241 [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(981, 1062890, F9, 2, 14) (dual of [(1062890, 2), 2125699, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(981, 1062890, F9, 3, 14) (dual of [(1062890, 3), 3188589, 15]-NRT-code) | [i] | ||
| 3 | Digital (67, 81, 1062890)-net over F9 | [i] | ||
| 4 | Linear OOA(981, 531445, F9, 2, 14) (dual of [(531445, 2), 1062809, 15]-NRT-code) | [i] | OOA Folding | |