Information on Result #724511
Linear OA(2567, 631, F25, 35) (dual of [631, 564, 36]-code), using construction XX applied to C1 = C([622,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([622,32]) based on
- linear OA(2564, 624, F25, 34) (dual of [624, 560, 35]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,31}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,32}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [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(5134, 1262, F5, 35) (dual of [1262, 1128, 36]-code) | [i] | Trace Code | |
| 2 | Linear OA(2588, 697, F25, 35) (dual of [697, 609, 36]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2589, 699, F25, 35) (dual of [699, 610, 36]-code) | [i] | ||
| 4 | Linear OA(2590, 701, F25, 35) (dual of [701, 611, 36]-code) | [i] | ||
| 5 | Linear OA(2591, 703, F25, 35) (dual of [703, 612, 36]-code) | [i] | ||
| 6 | Linear OA(2594, 757, F25, 35) (dual of [757, 663, 36]-code) | [i] | ||
| 7 | Linear OA(2595, 759, F25, 35) (dual of [759, 664, 36]-code) | [i] | ||
| 8 | Linear OA(2596, 761, F25, 35) (dual of [761, 665, 36]-code) | [i] | ||