Information on Result #1203448
Digital (13, 26, 2731)-net over F128, using net defined by OOA based on linear OOA(12826, 2731, F128, 13, 13) (dual of [(2731, 13), 35477, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12826, 16387, F128, 13) (dual of [16387, 16361, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(12826, 16390, F128, 13) (dual of [16390, 16364, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(12825, 16385, F128, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(12821, 16385, F128, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [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 C([0,6]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12826, 16390, F128, 13) (dual of [16390, 16364, 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 (14, 27, 2731)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (20, 33, 2881)-net over F128 | [i] | (u, u+v)-Construction for Nets | |