Information on Result #699576
Linear OA(8142, 6584, F81, 18) (dual of [6584, 6542, 19]-code), using construction X applied to Ce(17) ⊂ Ce(9) based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(817, 23, F81, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,81)), using
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), using
- Reed–Solomon code RS(74,81) [i]
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), 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(8142, 6584, F81, 2, 18) (dual of [(6584, 2), 13126, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8142, 6584, F81, 3, 18) (dual of [(6584, 3), 19710, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(8142, 6584, F81, 4, 18) (dual of [(6584, 4), 26294, 19]-NRT-code) | [i] | ||
| 4 | Digital (24, 42, 6584)-net over F81 | [i] | ||
| 5 | Linear OOA(8142, 3292, F81, 2, 18) (dual of [(3292, 2), 6542, 19]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8142, 2194, F81, 3, 18) (dual of [(2194, 3), 6540, 19]-NRT-code) | [i] | ||
| 7 | Linear OOA(8142, 1646, F81, 4, 18) (dual of [(1646, 4), 6542, 19]-NRT-code) | [i] | ||