Information on Result #992581
Linear OOA(12836, 5463, F128, 3, 18) (dual of [(5463, 3), 16353, 19]-NRT-code), using OOA 3-folding based on linear OA(12836, 16389, F128, 18) (dual of [16389, 16353, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-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 | Linear OOA(12846, 5613, F128, 3, 18) (dual of [(5613, 3), 16793, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12836, 4406, F128, 4, 18) (dual of [(4406, 4), 17588, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (18, 36, 4406)-net over F128 | [i] | ||