Information on Result #724337
Linear OA(2561, 631, F25, 32) (dual of [631, 570, 33]-code), using construction XX applied to C1 = C([622,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([622,29]) 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 = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [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 = {−2,−1,…,29}, and designed minimum distance d ≥ |I|+1 = 33 [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(251, 5, F25, 1) (dual of [5, 4, 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
- 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(5122, 1262, F5, 32) (dual of [1262, 1140, 33]-code) | [i] | Trace Code | |
| 2 | Linear OA(2581, 697, F25, 32) (dual of [697, 616, 33]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2582, 699, F25, 32) (dual of [699, 617, 33]-code) | [i] | ||
| 4 | Linear OA(2583, 701, F25, 32) (dual of [701, 618, 33]-code) | [i] | ||
| 5 | Linear OA(2584, 703, F25, 32) (dual of [703, 619, 33]-code) | [i] | ||
| 6 | Linear OA(2587, 757, F25, 32) (dual of [757, 670, 33]-code) | [i] | ||
| 7 | Linear OA(2588, 759, F25, 32) (dual of [759, 671, 33]-code) | [i] | ||