Information on Result #696579
Linear OA(3278, 1048585, F32, 20) (dual of [1048585, 1048507, 21]-code), using construction X applied to Ce(19) ⊂ Ce(17) based on
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 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 | Linear OA(3289, 1048629, F32, 20) (dual of [1048629, 1048540, 21]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3291, 1048649, F32, 20) (dual of [1048649, 1048558, 21]-code) | [i] | ||
| 3 | Linear OA(3294, 1048680, F32, 20) (dual of [1048680, 1048586, 21]-code) | [i] | ||
| 4 | Linear OA(3295, 1048683, F32, 20) (dual of [1048683, 1048588, 21]-code) | [i] | ||
| 5 | Linear OOA(3278, 669052, F32, 2, 20) (dual of [(669052, 2), 1338026, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (58, 78, 669052)-net over F32 | [i] | ||
| 7 | Linear OOA(3278, 524292, F32, 2, 20) (dual of [(524292, 2), 1048506, 21]-NRT-code) | [i] | OOA Folding | |