Information on Result #699726
Linear OA(12859, 2097159, F128, 20) (dual of [2097159, 2097100, 21]-code), using construction X applied to Ce(19) ⊂ Ce(17) based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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
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(16104, 2097159, S16, 20) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3283, 2097159, S32, 20) | [i] | ||
| 3 | OA(6469, 2097159, S64, 20) | [i] | ||
| 4 | Linear OA(12870, 2097309, F128, 20) (dual of [2097309, 2097239, 21]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12872, 2097351, F128, 20) (dual of [2097351, 2097279, 21]-code) | [i] | ||
| 6 | Linear OA(12875, 2097542, F128, 20) (dual of [2097542, 2097467, 21]-code) | [i] | ||
| 7 | Linear OA(12876, 2097545, F128, 20) (dual of [2097545, 2097469, 21]-code) | [i] | ||
| 8 | Linear OOA(12859, 1048579, F128, 2, 20) (dual of [(1048579, 2), 2097099, 21]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12859, 699053, F128, 3, 20) (dual of [(699053, 3), 2097100, 21]-NRT-code) | [i] | ||
| 10 | Linear OOA(12859, 524289, F128, 4, 20) (dual of [(524289, 4), 2097097, 21]-NRT-code) | [i] | ||