Information on Result #1561744
Linear OOA(9117, 1062890, F9, 3, 20) (dual of [(1062890, 3), 3188553, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9117, 1062890, F9, 20) (dual of [1062890, 1062773, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9116, 1062888, F9, 20) (dual of [1062888, 1062772, 21]-code), using
- trace code [i] based on linear OA(8158, 531444, F81, 20) (dual of [531444, 531386, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8155, 531441, F81, 19) (dual of [531441, 531386, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- trace code [i] based on linear OA(8158, 531444, F81, 20) (dual of [531444, 531386, 21]-code), using
- linear OA(9116, 1062889, F9, 19) (dual of [1062889, 1062773, 20]-code), using Gilbert–Varšamov bound and bm = 9116 > Vbs−1(k−1) = 8 433196 487574 581165 533227 011199 449249 023044 557887 994003 798236 779609 378115 738877 206429 371692 109837 934049 073729 [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
- linear OA(9116, 1062888, F9, 20) (dual of [1062888, 1062772, 21]-code), 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(9117, 265722, F9, 27, 20) (dual of [(265722, 27), 7174377, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |