Information on Result #1449934
Linear OOA(981, 13134, F9, 2, 20) (dual of [(13134, 2), 26187, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(981, 13134, F9, 20) (dual of [13134, 13053, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(980, 13132, F9, 20) (dual of [13132, 13052, 21]-code), using
- trace code [i] based on linear OA(8140, 6566, F81, 20) (dual of [6566, 6526, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- 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(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(19) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(8140, 6566, F81, 20) (dual of [6566, 6526, 21]-code), using
- linear OA(980, 13133, F9, 19) (dual of [13133, 13053, 20]-code), using Gilbert–Varšamov bound and bm = 980 > Vbs−1(k−1) = 375 186158 805992 945468 489913 144530 796260 714022 396373 276480 841451 218893 023969 [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(980, 13132, F9, 20) (dual of [13132, 13052, 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(981, 6567, F9, 3, 20) (dual of [(6567, 3), 19620, 21]-NRT-code) | [i] | OOA Folding | |