Information on Result #1464947
Linear OOA(12870, 2097192, F128, 2, 21) (dual of [(2097192, 2), 4194314, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12870, 2097192, F128, 21) (dual of [2097192, 2097122, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,5]) [i] 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(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(1289, 39, F128, 9) (dual of [39, 30, 10]-code or 39-arc in PG(8,128)), using
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- Reed–Solomon code RS(119,128) [i]
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
Mode: 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(12870, 1048596, F128, 3, 21) (dual of [(1048596, 3), 3145718, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12870, 1048596, F128, 4, 21) (dual of [(1048596, 4), 4194314, 22]-NRT-code) | [i] | ||