Information on Result #699696
Linear OA(12861, 2097155, F128, 21) (dual of [2097155, 2097094, 22]-code), using construction X applied to Ce(20) ⊂ Ce(19) based on
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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
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 | OA(16107, 2097155, S16, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3286, 2097155, S32, 21) | [i] | ||
| 3 | OA(6472, 2097155, S64, 21) | [i] | ||
| 4 | Linear OA(12871, 2097284, F128, 21) (dual of [2097284, 2097213, 22]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12872, 2097305, F128, 21) (dual of [2097305, 2097233, 22]-code) | [i] | ||
| 6 | Linear OA(12873, 2097307, F128, 21) (dual of [2097307, 2097234, 22]-code) | [i] | ||
| 7 | Linear OA(12874, 2097347, F128, 21) (dual of [2097347, 2097273, 22]-code) | [i] | ||
| 8 | Linear OA(12875, 2097349, F128, 21) (dual of [2097349, 2097274, 22]-code) | [i] | ||
| 9 | Linear OA(12876, 2097413, F128, 21) (dual of [2097413, 2097337, 22]-code) | [i] | ||
| 10 | Linear OA(12877, 2097538, F128, 21) (dual of [2097538, 2097461, 22]-code) | [i] | ||
| 11 | Linear OA(12878, 2097541, F128, 21) (dual of [2097541, 2097463, 22]-code) | [i] | ||
| 12 | Linear OOA(12861, 1048577, F128, 2, 21) (dual of [(1048577, 2), 2097093, 22]-NRT-code) | [i] | OOA Folding | |