Information on Result #696503
Linear OA(3236, 1048596, F32, 9) (dual of [1048596, 1048560, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
- linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(3217, 1048577, F32, 5) (dual of [1048577, 1048560, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), 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 OOA(3236, 1048596, F32, 2, 9) (dual of [(1048596, 2), 2097156, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (27, 36, 1048596)-net over F32 | [i] | ||
| 3 | Linear OOA(3236, 524298, F32, 2, 9) (dual of [(524298, 2), 1048560, 10]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3236, 262148, F32, 9, 9) (dual of [(262148, 9), 2359296, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |