Information on Result #735778
Linear OA(12834, 16515, F128, 14) (dual of [16515, 16481, 15]-code), using (u, u+v)-construction based on
- linear OA(1287, 129, F128, 7) (dual of [129, 122, 8]-code or 129-arc in PG(6,128)), using
- extended Reed–Solomon code RSe(122,128) [i]
- the expurgated narrow-sense BCH-code C(I) with length 129 | 1282−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(12827, 16386, F128, 14) (dual of [16386, 16359, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [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(12834, 16515, F128, 2, 14) (dual of [(16515, 2), 32996, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12834, 16515, F128, 3, 14) (dual of [(16515, 3), 49511, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(12834, 16515, F128, 4, 14) (dual of [(16515, 4), 66026, 15]-NRT-code) | [i] | ||
| 4 | Digital (20, 34, 16515)-net over F128 | [i] | ||
| 5 | Linear OOA(12834, 8257, F128, 2, 14) (dual of [(8257, 2), 16480, 15]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12834, 5505, F128, 3, 14) (dual of [(5505, 3), 16481, 15]-NRT-code) | [i] | ||