Information on Result #1195128
Digital (39, 52, 21847)-net over F16, using net defined by OOA based on linear OOA(1652, 21847, F16, 13, 13) (dual of [(21847, 13), 283959, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(1652, 131083, F16, 13) (dual of [131083, 131031, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1652, 131084, F16, 13) (dual of [131084, 131032, 14]-code), using
- trace code [i] based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- trace code [i] based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1652, 131084, F16, 13) (dual of [131084, 131032, 14]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (40, 53, 21847)-net over F16 | [i] | Net Duplication | |
| 2 | Digital (41, 54, 21847)-net over F16 | [i] | ||