Information on Result #1303625
Linear OA(1627, 131078, F16, 7) (dual of [131078, 131051, 8]-code), using construction X with Varšamov bound based on
- linear OA(1626, 131076, F16, 7) (dual of [131076, 131050, 8]-code), using
- trace code [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- linear OA(1626, 131077, F16, 6) (dual of [131077, 131051, 7]-code), using Gilbert–Varšamov bound and bm = 1626 > Vbs−1(k−1) = 244826 778925 460333 687782 998016 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(836, 131078, S8, 7) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1627, 131078, F16, 2, 7) (dual of [(131078, 2), 262129, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (20, 27, 131078)-net over F16 | [i] | ||
| 4 | Linear OOA(1627, 65539, F16, 2, 7) (dual of [(65539, 2), 131051, 8]-NRT-code) | [i] | OOA Folding | |