Information on Result #699683
Linear OA(12868, 2097184, F128, 21) (dual of [2097184, 2097116, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- linear OA(12861, 2097153, F128, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), 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(3296, 2097184, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6480, 2097184, S64, 21) | [i] | ||
| 3 | Linear OOA(12868, 1683051, F128, 2, 21) (dual of [(1683051, 2), 3366034, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(12868, 1683051, F128, 3, 21) (dual of [(1683051, 3), 5049085, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(12868, 1683051, F128, 4, 21) (dual of [(1683051, 4), 6732136, 22]-NRT-code) | [i] | ||
| 6 | Digital (47, 68, 1683051)-net over F128 | [i] | ||
| 7 | Linear OOA(12868, 1048592, F128, 2, 21) (dual of [(1048592, 2), 2097116, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(12868, 699061, F128, 3, 21) (dual of [(699061, 3), 2097115, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(12868, 524296, F128, 4, 21) (dual of [(524296, 4), 2097116, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(12868, 209718, F128, 21, 21) (dual of [(209718, 21), 4404010, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |