Information on Result #1464821
Linear OOA(12862, 2057335, F128, 2, 19) (dual of [(2057335, 2), 4114608, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12862, 2057335, F128, 19) (dual of [2057335, 2057273, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(12862, 2097184, F128, 19) (dual of [2097184, 2097122, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,5]) [i] 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(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(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
- construction X applied to C([0,9]) ⊂ C([0,5]) [i] based on
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(12862, 1028667, F128, 3, 19) (dual of [(1028667, 3), 3085939, 20]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12862, 1028667, F128, 4, 19) (dual of [(1028667, 4), 4114606, 20]-NRT-code) | [i] | ||