Information on Result #1070617
Linear OOA(12844, 4097, F128, 4, 22) (dual of [(4097, 4), 16344, 23]-NRT-code), using OOA 4-folding based on linear OA(12844, 16388, F128, 22) (dual of [16388, 16344, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12844, 16389, F128, 22) (dual of [16389, 16345, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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
- construction X applied to Ce(21) ⊂ Ce(19) [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(12856, 4247, F128, 4, 22) (dual of [(4247, 4), 16932, 23]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12858, 4289, F128, 4, 22) (dual of [(4289, 4), 17098, 23]-NRT-code) | [i] | ||
| 3 | Digital (22, 44, 4097)-net over F128 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |