Information on Result #862153
Linear OOA(2556, 314, F25, 2, 30) (dual of [(314, 2), 572, 31]-NRT-code), using OOA 2-folding based on 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]) [i] 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 OOA(2571, 340, F25, 2, 30) (dual of [(340, 2), 609, 31]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2572, 341, F25, 2, 30) (dual of [(341, 2), 610, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2573, 342, F25, 2, 30) (dual of [(342, 2), 611, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2574, 366, F25, 2, 30) (dual of [(366, 2), 658, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2575, 380, F25, 2, 30) (dual of [(380, 2), 685, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2580, 418, F25, 2, 30) (dual of [(418, 2), 756, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(2581, 440, F25, 2, 30) (dual of [(440, 2), 799, 31]-NRT-code) | [i] | ||
| 8 | Digital (26, 56, 271)-net over F25 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |