Information on Result #699678
Linear OA(12860, 2097176, F128, 19) (dual of [2097176, 2097116, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(12855, 2097153, F128, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12837, 2097153, F128, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(3284, 2097176, S32, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6470, 2097176, S64, 19) | [i] | ||
| 3 | Linear OOA(12860, 1162510, F128, 2, 19) (dual of [(1162510, 2), 2324960, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(12860, 1162510, F128, 3, 19) (dual of [(1162510, 3), 3487470, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(12860, 1162510, F128, 4, 19) (dual of [(1162510, 4), 4649980, 20]-NRT-code) | [i] | ||
| 6 | Digital (41, 60, 1162510)-net over F128 | [i] | ||
| 7 | Linear OOA(12860, 1048588, F128, 2, 19) (dual of [(1048588, 2), 2097116, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(12860, 699058, F128, 3, 19) (dual of [(699058, 3), 2097114, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(12860, 524294, F128, 4, 19) (dual of [(524294, 4), 2097116, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(12860, 233019, F128, 19, 19) (dual of [(233019, 19), 4427301, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |