Information on Result #992288
Linear OOA(12822, 699051, F128, 3, 8) (dual of [(699051, 3), 2097131, 9]-NRT-code), using OOA 3-folding based on linear OA(12822, 2097153, F128, 8) (dual of [2097153, 2097131, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [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(12826, 699180, F128, 3, 8) (dual of [(699180, 3), 2097514, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12827, 699201, F128, 3, 8) (dual of [(699201, 3), 2097576, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(12828, 707179, F128, 3, 8) (dual of [(707179, 3), 2121509, 9]-NRT-code) | [i] | ||
| 4 | OOA(12875, 3495252, S128, 3, 16) | [i] | ||
| 5 | OOA(12878, 3495252, S128, 3, 17) | [i] | ||
| 6 | Linear OOA(12844, large, F128, 3, 8) | [i] | Generalized (u, u+v)-Construction for OOAs | |