Information on Result #723359
Linear OA(2529, 628, F25, 15) (dual of [628, 599, 16]-code), using construction XX applied to C1 = C([623,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([623,13]) based on
- linear OA(2527, 624, F25, 14) (dual of [624, 597, 15]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2527, 624, F25, 14) (dual of [624, 597, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2529, 624, F25, 15) (dual of [624, 595, 16]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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(558, 1256, F5, 15) (dual of [1256, 1198, 16]-code) | [i] | Trace Code | |
| 2 | Linear OA(2536, 654, F25, 15) (dual of [654, 618, 16]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2537, 657, F25, 15) (dual of [657, 620, 16]-code) | [i] | ||
| 4 | Linear OA(2538, 659, F25, 15) (dual of [659, 621, 16]-code) | [i] | ||
| 5 | Linear OA(2539, 680, F25, 15) (dual of [680, 641, 16]-code) | [i] | ||
| 6 | Linear OA(2540, 706, F25, 15) (dual of [706, 666, 16]-code) | [i] | ||
| 7 | Linear OA(2541, 709, F25, 15) (dual of [709, 668, 16]-code) | [i] | ||
| 8 | Linear OA(2533, 654, F25, 15) (dual of [654, 621, 16]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(2534, 704, F25, 15) (dual of [704, 670, 16]-code) | [i] | ||
| 10 | Linear OA(2535, 816, F25, 15) (dual of [816, 781, 16]-code) | [i] | ||
| 11 | Linear OA(2536, 1002, F25, 15) (dual of [1002, 966, 16]-code) | [i] | ||
| 12 | Linear OOA(2529, 314, F25, 2, 15) (dual of [(314, 2), 599, 16]-NRT-code) | [i] | OOA Folding | |