Information on Result #695107
Linear OA(2710, 19686, F27, 4) (dual of [19686, 19676, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(2710, 19683, F27, 4) (dual of [19683, 19673, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(277, 19683, F27, 3) (dual of [19683, 19676, 4]-code or 19683-cap in PG(6,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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(915, 19686, S9, 4) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(2710, 19686, F27, 2, 4) (dual of [(19686, 2), 39362, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (6, 10, 19686)-net over F27 | [i] | ||
| 4 | Linear OOA(2710, 9843, F27, 2, 4) (dual of [(9843, 2), 19676, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2710, 9843, F27, 4, 4) (dual of [(9843, 4), 39362, 5]-NRT-code) | [i] | OA Folding and Stacking | |