Information on Result #1196948
Digital (53, 78, 1304)-net over F25, using net defined by OOA based on linear OOA(2578, 1304, F25, 25, 25) (dual of [(1304, 25), 32522, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2578, 15649, F25, 25) (dual of [15649, 15571, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2555, 15626, F25, 19) (dual of [15626, 15571, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
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 (54, 78, 1304)-net over F25 | [i] | t-Expansion | |
| 2 | Digital (54, 79, 1304)-net over F25 | [i] | Net Duplication | |
| 3 | Digital (55, 80, 1304)-net over F25 | [i] | ||
| 4 | Digital (56, 81, 1304)-net over F25 | [i] | ||
| 5 | Digital (57, 82, 1304)-net over F25 | [i] | ||
| 6 | Digital (58, 83, 1304)-net over F25 | [i] | ||
| 7 | Digital (53, 77, 1304)-net over F25 | [i] | m-Reduction | |