Information on Result #904870
Linear OOA(12858, 8388602, F128, 2, 11) (dual of [(8388602, 2), 16777146, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12817, 4194301, F128, 2, 5) (dual of [(4194301, 2), 8388585, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12817, 8388602, F128, 5) (dual of [8388602, 8388585, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(12817, large, F128, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(12817, large, F128, 5) (dual of [large, large−17, 6]-code), using
- OOA 2-folding [i] based on linear OA(12817, 8388602, F128, 5) (dual of [8388602, 8388585, 6]-code), using
- linear OOA(12841, 4194301, F128, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12841, 8388602, F128, 11) (dual of [8388602, 8388561, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- OOA 2-folding [i] based on linear OA(12841, 8388602, F128, 11) (dual of [8388602, 8388561, 12]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(12860, large, F128, 2, 11) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(12862, large, F128, 2, 11) | [i] | ||
| 3 | Linear OOA(12864, large, F128, 2, 11) | [i] | ||
| 4 | Linear OOA(12866, large, F128, 2, 11) | [i] | ||
| 5 | Linear OOA(12868, large, F128, 2, 11) | [i] | ||
| 6 | Linear OOA(12870, large, F128, 2, 11) | [i] | ||
| 7 | Linear OOA(12872, large, F128, 2, 11) | [i] | ||
| 8 | Linear OOA(12874, large, F128, 2, 11) | [i] | ||
| 9 | Linear OOA(12876, large, F128, 2, 11) | [i] | ||
| 10 | Linear OOA(12878, large, F128, 2, 11) | [i] | ||
| 11 | Linear OOA(12859, 8388602, F128, 2, 11) (dual of [(8388602, 2), 16777145, 12]-NRT-code) | [i] | OOA Duplication | |
| 12 | Linear OOA(12858, 4194301, F128, 3, 11) (dual of [(4194301, 3), 12582845, 12]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(12858, 4194301, F128, 4, 11) (dual of [(4194301, 4), 16777146, 12]-NRT-code) | [i] | ||
| 14 | Linear OOA(12858, 2796200, F128, 14, 11) (dual of [(2796200, 14), 39146742, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |