Information on Result #992254
Linear OOA(12816, 699051, F128, 3, 6) (dual of [(699051, 3), 2097137, 7]-NRT-code), using OOA 3-folding based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [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(12819, 699180, F128, 3, 6) (dual of [(699180, 3), 2097521, 7]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12820, 715436, F128, 3, 6) (dual of [(715436, 3), 2146288, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(12861, 3495252, F128, 3, 12) (dual of [(3495252, 3), 10485695, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(12865, 3495252, F128, 3, 13) (dual of [(3495252, 3), 10485691, 14]-NRT-code) | [i] | ||
| 5 | OOA(12855, 3495252, S128, 3, 12) | [i] | ||
| 6 | OOA(12859, 3495252, S128, 3, 13) | [i] | ||
| 7 | Linear OOA(12828, 6941863, F128, 3, 6) (dual of [(6941863, 3), 20825561, 7]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 8 | Linear OOA(12829, large, F128, 3, 6) | [i] | ||
| 9 | Linear OOA(12878, 6990510, F128, 3, 12) (dual of [(6990510, 3), 20971452, 13]-NRT-code) | [i] | ||
| 10 | Linear OOA(12877, 6291459, F128, 3, 12) (dual of [(6291459, 3), 18874300, 13]-NRT-code) | [i] | ||