Information on Result #735840
Linear OA(12829, 2097284, F128, 9) (dual of [2097284, 2097255, 10]-code), using (u, u+v)-construction based on
- linear OA(1284, 129, F128, 4) (dual of [129, 125, 5]-code or 129-arc in PG(3,128)), using
- extended Reed–Solomon code RSe(125,128) [i]
- linear OA(12825, 2097155, F128, 9) (dual of [2097155, 2097130, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(8) ⊂ Ce(7) [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(12829, 2097284, F128, 2, 9) (dual of [(2097284, 2), 4194539, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12829, 2097284, F128, 3, 9) (dual of [(2097284, 3), 6291823, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(12829, 2097284, F128, 4, 9) (dual of [(2097284, 4), 8389107, 10]-NRT-code) | [i] | ||
| 4 | Digital (20, 29, 2097284)-net over F128 | [i] | ||
| 5 | Linear OOA(12829, 1048642, F128, 2, 9) (dual of [(1048642, 2), 2097255, 10]-NRT-code) | [i] | OOA Folding | |