Information on Result #992597
Linear OOA(12852, 699051, F128, 3, 18) (dual of [(699051, 3), 2097101, 19]-NRT-code), using OOA 3-folding based on linear OA(12852, 2097153, F128, 18) (dual of [2097153, 2097101, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
Mode: Constructive and 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(12861, 699180, F128, 3, 18) (dual of [(699180, 3), 2097479, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12862, 699201, F128, 3, 18) (dual of [(699201, 3), 2097541, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(12864, 699243, F128, 3, 18) (dual of [(699243, 3), 2097665, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(12865, 699309, F128, 3, 18) (dual of [(699309, 3), 2097862, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(12866, 699330, F128, 3, 18) (dual of [(699330, 3), 2097924, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(12867, 699351, F128, 3, 18) (dual of [(699351, 3), 2097986, 19]-NRT-code) | [i] | ||
| 7 | Linear OOA(12868, 699372, F128, 3, 18) (dual of [(699372, 3), 2098048, 19]-NRT-code) | [i] | ||
| 8 | Linear OOA(12868, 699438, F128, 3, 18) (dual of [(699438, 3), 2098246, 19]-NRT-code) | [i] | ||
| 9 | Linear OOA(12852, 699051, F128, 4, 18) (dual of [(699051, 4), 2796152, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 10 | Digital (34, 52, 699051)-net over F128 | [i] | ||