Information on Result #699718
Linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using construction X applied to Ce(5) ⊂ Ce(4) based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 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(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 | OA(1628, 2097155, S16, 6) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3223, 2097155, S32, 6) | [i] | ||
| 3 | OA(6419, 2097155, S64, 6) | [i] | ||
| 4 | Linear OA(12819, 2097285, F128, 6) (dual of [2097285, 2097266, 7]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12820, 2113540, F128, 6) (dual of [2113540, 2113520, 7]-code) | [i] | ||
| 6 | Linear OOA(12816, 1048577, F128, 2, 6) (dual of [(1048577, 2), 2097138, 7]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12816, 699051, F128, 3, 6) (dual of [(699051, 3), 2097137, 7]-NRT-code) | [i] | ||
| 8 | Linear OOA(12816, 699051, F128, 4, 6) (dual of [(699051, 4), 2796188, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 9 | Linear OOA(12816, 699051, F128, 6, 6) (dual of [(699051, 6), 4194290, 7]-NRT-code) | [i] | ||