Information on Result #699496
Linear OA(8118, 6572, F81, 8) (dual of [6572, 6554, 9]-code), using construction X applied to Ce(7) ⊂ Ce(3) 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(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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 OOA(8118, 6572, F81, 2, 8) (dual of [(6572, 2), 13126, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8118, 6572, F81, 3, 8) (dual of [(6572, 3), 19698, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(8118, 6572, F81, 4, 8) (dual of [(6572, 4), 26270, 9]-NRT-code) | [i] | ||
| 4 | Digital (10, 18, 6572)-net over F81 | [i] | ||
| 5 | Linear OOA(8118, 3286, F81, 2, 8) (dual of [(3286, 2), 6554, 9]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8118, 2190, F81, 3, 8) (dual of [(2190, 3), 6552, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(8118, 1643, F81, 4, 8) (dual of [(1643, 4), 6554, 9]-NRT-code) | [i] | ||
| 8 | Linear OOA(8118, 1643, F81, 8, 8) (dual of [(1643, 8), 13126, 9]-NRT-code) | [i] | OA Folding and Stacking | |