Information on Result #735799
Linear OA(12843, 2097284, F128, 13) (dual of [2097284, 2097241, 14]-code), using (u, u+v)-construction based on
- linear OA(1286, 129, F128, 6) (dual of [129, 123, 7]-code or 129-arc in PG(5,128)), using
- extended Reed–Solomon code RSe(123,128) [i]
- linear OA(12837, 2097155, F128, 13) (dual of [2097155, 2097118, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [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(12843, 2097284, F128, 2, 13) (dual of [(2097284, 2), 4194525, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12843, 2097284, F128, 3, 13) (dual of [(2097284, 3), 6291809, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(12843, 2097284, F128, 4, 13) (dual of [(2097284, 4), 8389093, 14]-NRT-code) | [i] | ||
| 4 | Digital (30, 43, 2097284)-net over F128 | [i] | ||
| 5 | Linear OOA(12843, 1048642, F128, 2, 13) (dual of [(1048642, 2), 2097241, 14]-NRT-code) | [i] | OOA Folding | |