Information on Result #1050920
Linear OOA(12813, 1048577, F128, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(12850, 3145727, F128, 4, 10) (dual of [(3145727, 4), 12582858, 11]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12854, 3145727, F128, 4, 11) (dual of [(3145727, 4), 12582854, 12]-NRT-code) | [i] | ||
| 3 | OOA(12845, 3145727, S128, 4, 10) | [i] | ||
| 4 | OOA(12849, 3145727, S128, 4, 11) | [i] | ||
| 5 | Linear OOA(12863, 7242232, F128, 4, 11) (dual of [(7242232, 4), 28968865, 12]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 6 | Linear OOA(12864, large, F128, 4, 11) | [i] | ||
| 7 | Linear OOA(12859, 7242232, F128, 4, 10) (dual of [(7242232, 4), 28968869, 11]-NRT-code) | [i] | ||
| 8 | Linear OOA(12860, large, F128, 4, 10) | [i] | ||
| 9 | Linear OOA(12820, large, F128, 4, 5) | [i] | ||
| 10 | Linear OOA(12862, 4718592, F128, 4, 11) (dual of [(4718592, 4), 18874306, 12]-NRT-code) | [i] | ||
| 11 | Linear OOA(12861, 4194304, F128, 4, 11) (dual of [(4194304, 4), 16777155, 12]-NRT-code) | [i] | ||
| 12 | Linear OOA(12860, 4194304, F128, 4, 11) (dual of [(4194304, 4), 16777156, 12]-NRT-code) | [i] | ||
| 13 | Linear OOA(12856, 4194304, F128, 4, 10) (dual of [(4194304, 4), 16777160, 11]-NRT-code) | [i] | ||
| 14 | Linear OOA(12813, 1048577, F128, 5, 5) (dual of [(1048577, 5), 5242872, 6]-NRT-code) | [i] | Appending kth Column | |