Information on Result #1560661
Linear OOA(989, 13134, F9, 3, 22) (dual of [(13134, 3), 39313, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(989, 13134, F9, 22) (dual of [13134, 13045, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(988, 13132, F9, 22) (dual of [13132, 13044, 23]-code), using
- trace code [i] based on linear OA(8144, 6566, F81, 22) (dual of [6566, 6522, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(8144, 6566, F81, 22) (dual of [6566, 6522, 23]-code), using
- linear OA(988, 13133, F9, 21) (dual of [13133, 13045, 22]-code), using Gilbert–Varšamov bound and bm = 988 > Vbs−1(k−1) = 10866 475840 009129 446712 231769 625490 802448 112523 821323 343049 049806 412212 865038 559969 [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(988, 13132, F9, 22) (dual of [13132, 13044, 23]-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(989, 3283, F9, 27, 22) (dual of [(3283, 27), 88552, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |