Information on Result #699942
Linear OA(1287, 16386, F128, 4) (dual of [16386, 16379, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1285, 16384, F128, 3) (dual of [16384, 16379, 4]-code or 16384-cap in PG(4,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(649, 16386, S64, 4) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(12824, 32772, F128, 9) (dual of [32772, 32748, 10]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(12832, 2113541, F128, 9) (dual of [2113541, 2113509, 10]-code) | [i] | ||
| 4 | Linear OA(12812, 2097408, F128, 4) (dual of [2097408, 2097396, 5]-code) | [i] | Generalized (u, u+v)-Construction | |
| 5 | Linear OOA(1287, 16386, F128, 2, 4) (dual of [(16386, 2), 32765, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(1287, 16386, F128, 3, 4) (dual of [(16386, 3), 49151, 5]-NRT-code) | [i] | ||
| 7 | Linear OOA(1287, 8193, F128, 2, 4) (dual of [(8193, 2), 16379, 5]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(1287, 8193, F128, 3, 4) (dual of [(8193, 3), 24572, 5]-NRT-code) | [i] | OA Folding and Stacking | |
| 9 | Linear OOA(1287, 8193, F128, 4, 4) (dual of [(8193, 4), 32765, 5]-NRT-code) | [i] | ||