Information on Result #735486
Linear OA(8119, 6645, F81, 8) (dual of [6645, 6626, 9]-code), using (u, u+v)-construction based on
- linear OA(814, 82, F81, 4) (dual of [82, 78, 5]-code or 82-arc in PG(3,81)), using
- extended Reed–Solomon code RSe(78,81) [i]
- linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [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(8119, 6645, F81, 2, 8) (dual of [(6645, 2), 13271, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8119, 6645, F81, 3, 8) (dual of [(6645, 3), 19916, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(8119, 6645, F81, 4, 8) (dual of [(6645, 4), 26561, 9]-NRT-code) | [i] | ||
| 4 | Digital (11, 19, 6645)-net over F81 | [i] | ||
| 5 | Linear OOA(8119, 3322, F81, 2, 8) (dual of [(3322, 2), 6625, 9]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8119, 2215, F81, 3, 8) (dual of [(2215, 3), 6626, 9]-NRT-code) | [i] | ||