Information on Result #699196
Linear OA(8117, 531449, F81, 6) (dual of [531449, 531432, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(817, 8, F81, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,81)), using
- dual of repetition code with length 8 [i]
- linear OA(811, 8, F81, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- Reed–Solomon code RS(80,81) [i]
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), 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 | Linear OA(934, 1062898, F9, 6) (dual of [1062898, 1062864, 7]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8117, 531449, F81, 2, 6) (dual of [(531449, 2), 1062881, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8117, 531449, F81, 3, 6) (dual of [(531449, 3), 1594330, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(8117, 531449, F81, 4, 6) (dual of [(531449, 4), 2125779, 7]-NRT-code) | [i] | ||
| 5 | Digital (11, 17, 531449)-net over F81 | [i] | ||