Information on Result #861370
Linear OOA(2539, 314, F25, 2, 20) (dual of [(314, 2), 589, 21]-NRT-code), using OOA 2-folding based on linear OA(2539, 628, F25, 20) (dual of [628, 589, 21]-code), using
- construction XX applied to C1 = C([623,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([623,18]) [i] based on
- linear OA(2537, 624, F25, 19) (dual of [624, 587, 20]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2537, 624, F25, 19) (dual of [624, 587, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2539, 624, F25, 20) (dual of [624, 585, 21]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2535, 624, F25, 18) (dual of [624, 589, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [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(2549, 340, F25, 2, 20) (dual of [(340, 2), 631, 21]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2550, 341, F25, 2, 20) (dual of [(341, 2), 632, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(2551, 342, F25, 2, 20) (dual of [(342, 2), 633, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(2552, 366, F25, 2, 20) (dual of [(366, 2), 680, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(2553, 380, F25, 2, 20) (dual of [(380, 2), 707, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(25104, 400, F25, 2, 40) (dual of [(400, 2), 696, 41]-NRT-code) | [i] | ||
| 7 | Linear OOA(25106, 402, F25, 2, 40) (dual of [(402, 2), 698, 41]-NRT-code) | [i] | ||
| 8 | Linear OOA(25108, 404, F25, 2, 40) (dual of [(404, 2), 700, 41]-NRT-code) | [i] | ||
| 9 | Linear OOA(25105, 400, F25, 2, 41) (dual of [(400, 2), 695, 42]-NRT-code) | [i] | ||
| 10 | Linear OOA(25107, 402, F25, 2, 41) (dual of [(402, 2), 697, 42]-NRT-code) | [i] | ||
| 11 | Linear OOA(25109, 404, F25, 2, 41) (dual of [(404, 2), 699, 42]-NRT-code) | [i] | ||
| 12 | Linear OOA(25110, 408, F25, 2, 41) (dual of [(408, 2), 706, 42]-NRT-code) | [i] | ||
| 13 | Digital (19, 39, 314)-net over F25 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |