Information on Result #724268
Linear OA(2562, 634, F25, 32) (dual of [634, 572, 33]-code), using construction XX applied to C1 = C([621,27]), C2 = C([0,28]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([621,28]) based on
- linear OA(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,27}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2554, 624, F25, 29) (dual of [624, 570, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,28}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2552, 624, F25, 28) (dual of [624, 572, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OA(5124, 1268, F5, 32) (dual of [1268, 1144, 33]-code) | [i] | Trace Code | |
| 2 | Linear OA(2582, 700, F25, 32) (dual of [700, 618, 33]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2583, 702, F25, 32) (dual of [702, 619, 33]-code) | [i] | ||
| 4 | Linear OA(2584, 704, F25, 32) (dual of [704, 620, 33]-code) | [i] | ||
| 5 | Linear OA(2588, 760, F25, 32) (dual of [760, 672, 33]-code) | [i] | ||
| 6 | Linear OOA(2562, 317, F25, 2, 32) (dual of [(317, 2), 572, 33]-NRT-code) | [i] | OOA Folding | |