Information on Result #699625
Linear OA(8170, 6596, F81, 30) (dual of [6596, 6526, 31]-code), using construction X applied to Ce(29) ⊂ Ce(17) based on
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(8111, 35, F81, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,81)), using
- discarding factors / shortening the dual code based on linear OA(8111, 81, F81, 11) (dual of [81, 70, 12]-code or 81-arc in PG(10,81)), using
- Reed–Solomon code RS(70,81) [i]
- discarding factors / shortening the dual code based on linear OA(8111, 81, F81, 11) (dual of [81, 70, 12]-code or 81-arc in PG(10,81)), 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(8170, 6596, F81, 2, 30) (dual of [(6596, 2), 13122, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8170, 6596, F81, 3, 30) (dual of [(6596, 3), 19718, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(8170, 6596, F81, 4, 30) (dual of [(6596, 4), 26314, 31]-NRT-code) | [i] | ||
| 4 | Digital (40, 70, 6596)-net over F81 | [i] | ||
| 5 | Linear OOA(8170, 3298, F81, 2, 30) (dual of [(3298, 2), 6526, 31]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8170, 2198, F81, 3, 30) (dual of [(2198, 3), 6524, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(8170, 1649, F81, 4, 30) (dual of [(1649, 4), 6526, 31]-NRT-code) | [i] | ||