Information on Result #693319
Linear OA(2520, 15634, F25, 7) (dual of [15634, 15614, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(2519, 15626, F25, 7) (dual of [15626, 15607, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2513, 15626, F25, 5) (dual of [15626, 15613, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(257, 8, F25, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,25)), using
- dual of repetition code with length 8 [i]
- linear OA(251, 8, F25, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), 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(2520, 15634, F25, 2, 7) (dual of [(15634, 2), 31248, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (13, 20, 15634)-net over F25 | [i] | ||
| 3 | Linear OOA(2520, 7817, F25, 2, 7) (dual of [(7817, 2), 15614, 8]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2520, 5211, F25, 7, 7) (dual of [(5211, 7), 36457, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |