Information on Result #735632
Linear OA(12851, 16515, F128, 21) (dual of [16515, 16464, 22]-code), using (u, u+v)-construction based on
- linear OA(12810, 129, F128, 10) (dual of [129, 119, 11]-code or 129-arc in PG(9,128)), using
- extended Reed–Solomon code RSe(119,128) [i]
- linear OA(12841, 16386, F128, 21) (dual of [16386, 16345, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(1280, 2, F128, 0) (dual of [2, 2, 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(20) ⊂ 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 | OA(6460, 16515, S64, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12851, 16515, F128, 2, 21) (dual of [(16515, 2), 32979, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12851, 16515, F128, 3, 21) (dual of [(16515, 3), 49494, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(12851, 16515, F128, 4, 21) (dual of [(16515, 4), 66009, 22]-NRT-code) | [i] | ||
| 5 | Digital (30, 51, 16515)-net over F128 | [i] | ||
| 6 | Linear OOA(12851, 5505, F128, 3, 21) (dual of [(5505, 3), 16464, 22]-NRT-code) | [i] | OOA Folding | |