Information on Result #991816
Linear OOA(8164, 2188, F81, 3, 32) (dual of [(2188, 3), 6500, 33]-NRT-code), using OOA 3-folding based on linear OA(8164, 6564, F81, 32) (dual of [6564, 6500, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(8164, 6566, F81, 32) (dual of [6566, 6502, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- 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(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(29) [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(8182, 2304, F81, 3, 32) (dual of [(2304, 3), 6830, 33]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8164, 2018, F81, 4, 32) (dual of [(2018, 4), 8008, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (32, 64, 2018)-net over F81 | [i] | ||