Information on Result #1522234
Linear OOA(3109, 9860, F3, 3, 17) (dual of [(9860, 3), 29471, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3109, 9860, F3, 2, 17) (dual of [(9860, 2), 19611, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3109, 19720, F3, 17) (dual of [19720, 19611, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3106, 19716, F3, 17) (dual of [19716, 19610, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3106, 19717, F3, 14) (dual of [19717, 19611, 15]-code), using Gilbert–Varšamov bound and bm = 3106 > Vbs−1(k−1) = 89 161820 477436 091068 580295 093548 707682 005999 461457 [i]
- linear OA(32, 3, F3, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)), using
- dual of repetition code with length 3 [i]
- Reed–Solomon code RS(1,3) [i]
- linear OA(3106, 19716, F3, 17) (dual of [19716, 19610, 18]-code), using
- construction X with Varšamov bound [i] based on
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(3109, 4930, F3, 5, 17) (dual of [(4930, 5), 24541, 18]-NRT-code) | [i] | OOA Folding | |