Information on Result #723615
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]) 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 OA(578, 1256, F5, 20) (dual of [1256, 1178, 21]-code) | [i] | Trace Code | |
| 2 | Linear OA(2552, 680, F25, 20) (dual of [680, 628, 21]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2553, 694, F25, 20) (dual of [694, 641, 21]-code) | [i] | ||
| 4 | Linear OA(2554, 696, F25, 20) (dual of [696, 642, 21]-code) | [i] | ||
| 5 | Linear OA(2555, 698, F25, 20) (dual of [698, 643, 21]-code) | [i] | ||
| 6 | Linear OA(2556, 734, F25, 20) (dual of [734, 678, 21]-code) | [i] | ||
| 7 | Linear OA(2543, 641, F25, 20) (dual of [641, 598, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(2544, 663, F25, 20) (dual of [663, 619, 21]-code) | [i] | ||
| 9 | Linear OA(2545, 717, F25, 20) (dual of [717, 672, 21]-code) | [i] | ||
| 10 | Linear OA(2546, 817, F25, 20) (dual of [817, 771, 21]-code) | [i] | ||
| 11 | Linear OA(2547, 959, F25, 20) (dual of [959, 912, 21]-code) | [i] | ||
| 12 | Linear OOA(2539, 314, F25, 2, 20) (dual of [(314, 2), 589, 21]-NRT-code) | [i] | OOA Folding | |