Information on Result #1050921
Linear OOA(12814, 1048580, F128, 4, 5) (dual of [(1048580, 4), 4194306, 6]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OA(12814, 2097161, F128, 5) (dual of [2097161, 2097147, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1287, 2097153, F128, 3) (dual of [2097153, 2097146, 4]-code or 2097153-cap in PG(6,128)), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(1287, 8, F128, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
- dual of repetition code with length 8 [i]
- linear OA(1281, 8, F128, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- Reed–Solomon code RS(127,128) [i]
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), 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 | Linear OOA(12851, 3145730, F128, 4, 10) (dual of [(3145730, 4), 12582869, 11]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12855, 3145730, F128, 4, 11) (dual of [(3145730, 4), 12582865, 12]-NRT-code) | [i] | ||
| 3 | OOA(12846, 3145730, S128, 4, 10) | [i] | ||
| 4 | OOA(12850, 3145730, S128, 4, 11) | [i] | ||
| 5 | Linear OOA(12861, 4194310, F128, 4, 11) (dual of [(4194310, 4), 16777179, 12]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 6 | Linear OOA(12857, 4194310, F128, 4, 10) (dual of [(4194310, 4), 16777183, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(12814, 1048580, F128, 5, 5) (dual of [(1048580, 5), 5242886, 6]-NRT-code) | [i] | Appending kth Column | |