Information on Result #878571
Linear OOA(12849, 1048577, F128, 2, 17) (dual of [(1048577, 2), 2097105, 18]-NRT-code), using OOA 2-folding based on linear OA(12849, 2097154, F128, 17) (dual of [2097154, 2097105, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(12849, 2097155, F128, 17) (dual of [2097155, 2097106, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 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(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(16) ⊂ Ce(15) [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(12857, 1048706, F128, 2, 17) (dual of [(1048706, 2), 2097355, 18]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12858, 1048727, F128, 2, 17) (dual of [(1048727, 2), 2097396, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(12860, 1048769, F128, 2, 17) (dual of [(1048769, 2), 2097478, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(12861, 1048835, F128, 2, 17) (dual of [(1048835, 2), 2097609, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(12862, 1048856, F128, 2, 17) (dual of [(1048856, 2), 2097650, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(12863, 1048877, F128, 2, 17) (dual of [(1048877, 2), 2097691, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(12863, 1048964, F128, 2, 17) (dual of [(1048964, 2), 2097865, 18]-NRT-code) | [i] | ||