Information on Result #724266
Linear OA(2556, 628, F25, 30) (dual of [628, 572, 31]-code), using construction XX applied to C1 = C([623,27]), C2 = C([0,28]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([623,28]) based on
- linear OA(2554, 624, F25, 29) (dual of [624, 570, 30]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [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(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [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(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(5112, 1256, F5, 30) (dual of [1256, 1144, 31]-code) | [i] | Trace Code | |
| 2 | Linear OA(2574, 680, F25, 30) (dual of [680, 606, 31]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2575, 694, F25, 30) (dual of [694, 619, 31]-code) | [i] | ||
| 4 | Linear OA(2576, 696, F25, 30) (dual of [696, 620, 31]-code) | [i] | ||
| 5 | Linear OA(2577, 698, F25, 30) (dual of [698, 621, 31]-code) | [i] | ||
| 6 | Linear OA(2578, 700, F25, 30) (dual of [700, 622, 31]-code) | [i] | ||
| 7 | Linear OA(2579, 702, F25, 30) (dual of [702, 623, 31]-code) | [i] | ||
| 8 | Linear OA(2580, 732, F25, 30) (dual of [732, 652, 31]-code) | [i] | ||
| 9 | Linear OA(2581, 754, F25, 30) (dual of [754, 673, 31]-code) | [i] | ||
| 10 | Linear OA(2582, 756, F25, 30) (dual of [756, 674, 31]-code) | [i] | ||
| 11 | Linear OA(2583, 788, F25, 30) (dual of [788, 705, 31]-code) | [i] | ||
| 12 | Linear OA(2563, 652, F25, 30) (dual of [652, 589, 31]-code) | [i] | Varšamov–Edel Lengthening | |
| 13 | Linear OA(2564, 672, F25, 30) (dual of [672, 608, 31]-code) | [i] | ||
| 14 | Linear OA(2565, 708, F25, 30) (dual of [708, 643, 31]-code) | [i] | ||
| 15 | Linear OA(2566, 765, F25, 30) (dual of [765, 699, 31]-code) | [i] | ||
| 16 | Linear OA(2567, 843, F25, 30) (dual of [843, 776, 31]-code) | [i] | ||
| 17 | Linear OOA(2556, 314, F25, 2, 30) (dual of [(314, 2), 572, 31]-NRT-code) | [i] | OOA Folding | |