Information on Result #878344
Linear OOA(12820, 8194, F128, 2, 10) (dual of [(8194, 2), 16368, 11]-NRT-code), using OOA 2-folding based on linear OA(12820, 16388, F128, 10) (dual of [16388, 16368, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(12820, 16389, F128, 10) (dual of [16389, 16369, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
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(12820, 6974, F128, 3, 10) (dual of [(6974, 3), 20902, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12820, 6974, F128, 4, 10) (dual of [(6974, 4), 27876, 11]-NRT-code) | [i] | ||
| 3 | Digital (10, 20, 6974)-net over F128 | [i] | ||