Information on Result #1196526
Digital (37, 54, 1956)-net over F25, using net defined by OOA based on linear OOA(2554, 1956, F25, 17, 17) (dual of [(1956, 17), 33198, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2554, 15649, F25, 17) (dual of [15649, 15595, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(2549, 15626, F25, 17) (dual of [15626, 15577, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2531, 15626, F25, 11) (dual of [15626, 15595, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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([0,8]) ⊂ C([0,5]) [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 (38, 55, 1956)-net over F25 | [i] | Net Duplication | |
| 2 | Digital (39, 56, 1956)-net over F25 | [i] | ||
| 3 | Digital (37, 53, 1956)-net over F25 | [i] | m-Reduction | |