Information on Result #862442
Linear OOA(2564, 314, F25, 2, 34) (dual of [(314, 2), 564, 35]-NRT-code), using OOA 2-folding based on linear OA(2564, 628, F25, 34) (dual of [628, 564, 35]-code), using
- construction XX applied to C1 = C([623,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([623,32]) [i] based on
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [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(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 = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [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(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(2581, 340, F25, 2, 34) (dual of [(340, 2), 599, 35]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2582, 341, F25, 2, 34) (dual of [(341, 2), 600, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2583, 342, F25, 2, 34) (dual of [(342, 2), 601, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2584, 366, F25, 2, 34) (dual of [(366, 2), 648, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2585, 380, F25, 2, 34) (dual of [(380, 2), 675, 35]-NRT-code) | [i] | ||
| 6 | Linear OOA(2590, 418, F25, 2, 34) (dual of [(418, 2), 746, 35]-NRT-code) | [i] | ||
| 7 | Linear OOA(2591, 440, F25, 2, 34) (dual of [(440, 2), 789, 35]-NRT-code) | [i] | ||
| 8 | Digital (30, 64, 308)-net over F25 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |