Information on Result #724460
Linear OA(2562, 628, F25, 33) (dual of [628, 566, 34]-code), using construction XX applied to C1 = C([623,30]), C2 = C([0,31]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([623,31]) based on
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [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(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(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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(5124, 1256, F5, 33) (dual of [1256, 1132, 34]-code) | [i] | Trace Code | |
| 2 | Linear OA(2581, 680, F25, 33) (dual of [680, 599, 34]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2582, 694, F25, 33) (dual of [694, 612, 34]-code) | [i] | ||
| 4 | Linear OA(2583, 696, F25, 33) (dual of [696, 613, 34]-code) | [i] | ||
| 5 | Linear OA(2584, 698, F25, 33) (dual of [698, 614, 34]-code) | [i] | ||
| 6 | Linear OA(2585, 700, F25, 33) (dual of [700, 615, 34]-code) | [i] | ||
| 7 | Linear OA(2586, 702, F25, 33) (dual of [702, 616, 34]-code) | [i] | ||
| 8 | Linear OA(2587, 732, F25, 33) (dual of [732, 645, 34]-code) | [i] | ||
| 9 | Linear OA(2588, 754, F25, 33) (dual of [754, 666, 34]-code) | [i] | ||
| 10 | Linear OA(2589, 756, F25, 33) (dual of [756, 667, 34]-code) | [i] | ||
| 11 | Linear OA(2590, 758, F25, 33) (dual of [758, 668, 34]-code) | [i] | ||
| 12 | Linear OA(2591, 788, F25, 33) (dual of [788, 697, 34]-code) | [i] | ||
| 13 | Linear OA(2592, 944, F25, 33) (dual of [944, 852, 34]-code) | [i] | ||
| 14 | Linear OA(2569, 652, F25, 33) (dual of [652, 583, 34]-code) | [i] | Varšamov–Edel Lengthening | |
| 15 | Linear OA(2570, 674, F25, 33) (dual of [674, 604, 34]-code) | [i] | ||
| 16 | Linear OA(2571, 711, F25, 33) (dual of [711, 640, 34]-code) | [i] | ||
| 17 | Linear OA(2572, 767, F25, 33) (dual of [767, 695, 34]-code) | [i] | ||
| 18 | Linear OA(2573, 841, F25, 33) (dual of [841, 768, 34]-code) | [i] | ||
| 19 | Linear OOA(2562, 314, F25, 2, 33) (dual of [(314, 2), 566, 34]-NRT-code) | [i] | OOA Folding | |