Information on Result #691529
Linear OA(1672, 1048588, F16, 15) (dual of [1048588, 1048516, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(1671, 1048577, F16, 15) (dual of [1048577, 1048506, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(1661, 1048577, F16, 13) (dual of [1048577, 1048516, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1672, 1048588, F16, 2, 15) (dual of [(1048588, 2), 2097104, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (57, 72, 1048588)-net over F16 | [i] | ||
| 3 | Linear OOA(1672, 524294, F16, 2, 15) (dual of [(524294, 2), 1048516, 16]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(1672, 149798, F16, 15, 15) (dual of [(149798, 15), 2246898, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |