Information on Result #699939
Linear OA(12813, 16386, F128, 7) (dual of [16386, 16373, 8]-code), using construction X applied to Ce(6) ⊂ Ce(5) based on
- linear OA(12813, 16384, F128, 7) (dual of [16384, 16371, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 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 | OA(1623, 16386, S16, 7) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6416, 16386, S64, 7) | [i] | ||
| 3 | Linear OA(12842, 32772, F128, 15) (dual of [32772, 32730, 16]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(12856, 2113541, F128, 15) (dual of [2113541, 2113485, 16]-code) | [i] | ||
| 5 | Linear OA(12816, 16516, F128, 7) (dual of [16516, 16500, 8]-code) | [i] | ||
| 6 | Linear OA(12817, 32771, F128, 7) (dual of [32771, 32754, 8]-code) | [i] | ||
| 7 | Linear OOA(12813, 8193, F128, 2, 7) (dual of [(8193, 2), 16373, 8]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(12813, 5462, F128, 3, 7) (dual of [(5462, 3), 16373, 8]-NRT-code) | [i] | ||