Information on Result #724815
Linear OA(2578, 628, F25, 41) (dual of [628, 550, 42]-code), using construction XX applied to C1 = C([623,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([623,39]) based on
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,38}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,39}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- 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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
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(25102, 694, F25, 41) (dual of [694, 592, 42]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(25103, 696, F25, 41) (dual of [696, 593, 42]-code) | [i] | ||
| 3 | Linear OA(25104, 698, F25, 41) (dual of [698, 594, 42]-code) | [i] | ||
| 4 | Linear OA(25105, 700, F25, 41) (dual of [700, 595, 42]-code) | [i] | ||
| 5 | Linear OA(25106, 702, F25, 41) (dual of [702, 596, 42]-code) | [i] | ||
| 6 | Linear OA(25107, 732, F25, 41) (dual of [732, 625, 42]-code) | [i] | ||
| 7 | Linear OA(25108, 754, F25, 41) (dual of [754, 646, 42]-code) | [i] | ||
| 8 | Linear OA(25109, 756, F25, 41) (dual of [756, 647, 42]-code) | [i] | ||
| 9 | Linear OA(25110, 758, F25, 41) (dual of [758, 648, 42]-code) | [i] | ||
| 10 | Linear OA(2585, 663, F25, 41) (dual of [663, 578, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(2586, 695, F25, 41) (dual of [695, 609, 42]-code) | [i] | ||
| 12 | Linear OA(2587, 743, F25, 41) (dual of [743, 656, 42]-code) | [i] | ||
| 13 | Linear OOA(2578, 314, F25, 2, 41) (dual of [(314, 2), 550, 42]-NRT-code) | [i] | OOA Folding | |