Information on Result #723103
Linear OA(2515, 628, F25, 8) (dual of [628, 613, 9]-code), using construction XX applied to C1 = C([623,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([623,6]) based on
- linear OA(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [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(2564, 16256, F25, 17) (dual of [16256, 16192, 18]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2580, 391257, F25, 17) (dual of [391257, 391177, 18]-code) | [i] | ||
| 3 | Linear OA(2519, 654, F25, 8) (dual of [654, 635, 9]-code) | [i] | ||
| 4 | Linear OA(2520, 657, F25, 8) (dual of [657, 637, 9]-code) | [i] | ||
| 5 | Linear OA(2517, 641, F25, 8) (dual of [641, 624, 9]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(2518, 705, F25, 8) (dual of [705, 687, 9]-code) | [i] | ||
| 7 | Linear OA(2519, 922, F25, 8) (dual of [922, 903, 9]-code) | [i] | ||
| 8 | Linear OA(2520, 1400, F25, 8) (dual of [1400, 1380, 9]-code) | [i] | ||
| 9 | Linear OOA(2515, 314, F25, 2, 8) (dual of [(314, 2), 613, 9]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(2515, 157, F25, 8, 8) (dual of [(157, 8), 1241, 9]-NRT-code) | [i] | OA Folding and Stacking | |