Information on Result #722646
Linear OA(1615, 825, F16, 6) (dual of [825, 810, 7]-code), using construction XX applied to C1 = C([106,110]), C2 = C([105,109]), C3 = C1 + C2 = C([106,109]), and C∩ = C1 ∩ C2 = C([105,110]) based on
- linear OA(1612, 819, F16, 5) (dual of [819, 807, 6]-code), using the BCH-code C(I) with length 819 | 163−1, defining interval I = {106,107,108,109,110}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1612, 819, F16, 5) (dual of [819, 807, 6]-code), using the BCH-code C(I) with length 819 | 163−1, defining interval I = {105,106,107,108,109}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1615, 819, F16, 6) (dual of [819, 804, 7]-code), using the BCH-code C(I) with length 819 | 163−1, defining interval I = {105,106,…,110}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(169, 819, F16, 4) (dual of [819, 810, 5]-code), using the BCH-code C(I) with length 819 | 163−1, defining interval I = {106,107,108,109}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code) (see above)
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 | OA(820, 825, S8, 6) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1615, 825, F16, 2, 6) (dual of [(825, 2), 1635, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (9, 15, 825)-net over F16 | [i] | ||
| 4 | Linear OOA(1615, 412, F16, 2, 6) (dual of [(412, 2), 809, 7]-NRT-code) | [i] | OOA Folding | |