Information on Result #721315
Linear OA(1618, 89, F16, 10) (dual of [89, 71, 11]-code), using construction XX applied to C1 = C([4,12]), C2 = C([3,11]), C3 = C1 + C2 = C([4,11]), and C∩ = C1 ∩ C2 = C([3,12]) based on
- linear OA(1616, 85, F16, 9) (dual of [85, 69, 10]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,12}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1616, 85, F16, 9) (dual of [85, 69, 10]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {3,4,…,11}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1618, 85, F16, 10) (dual of [85, 67, 11]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {3,4,…,12}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1614, 85, F16, 8) (dual of [85, 71, 9]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,11}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 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, 2, F16, 0) (dual of [2, 2, 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 | Linear OA(16114, 1048670, F16, 21) (dual of [1048670, 1048556, 22]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1618, 88, F16, 2, 10) (dual of [(88, 2), 158, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (8, 18, 88)-net over F16 | [i] | ||
| 4 | Linear OOA(1618, 44, F16, 2, 10) (dual of [(44, 2), 70, 11]-NRT-code) | [i] | OOA Folding | |