Information on Result #699679
Linear OA(12854, 2097176, F128, 17) (dual of [2097176, 2097122, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12831, 2097153, F128, 11) (dual of [2097153, 2097122, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), 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 | OA(3276, 2097176, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6463, 2097176, S64, 17) | [i] | ||
| 3 | Linear OOA(12854, 1410705, F128, 2, 17) (dual of [(1410705, 2), 2821356, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(12854, 1410705, F128, 3, 17) (dual of [(1410705, 3), 4232061, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(12854, 1410705, F128, 4, 17) (dual of [(1410705, 4), 5642766, 18]-NRT-code) | [i] | ||
| 6 | Digital (37, 54, 1410705)-net over F128 | [i] | ||
| 7 | Linear OOA(12854, 1048588, F128, 2, 17) (dual of [(1048588, 2), 2097122, 18]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(12854, 699058, F128, 3, 17) (dual of [(699058, 3), 2097120, 18]-NRT-code) | [i] | ||
| 9 | Linear OOA(12854, 524294, F128, 4, 17) (dual of [(524294, 4), 2097122, 18]-NRT-code) | [i] | ||