Information on Result #724402
Linear OA(2566, 634, F25, 34) (dual of [634, 568, 35]-code), using construction XX applied to C1 = C([621,29]), C2 = C([0,30]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([621,30]) based on
- 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 = {−3,−2,…,29}, 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(2564, 624, F25, 34) (dual of [624, 560, 35]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,30}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- 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
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(5132, 1268, F5, 34) (dual of [1268, 1136, 35]-code) | [i] | Trace Code | |
| 2 | Linear OA(2587, 700, F25, 34) (dual of [700, 613, 35]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2588, 702, F25, 34) (dual of [702, 614, 35]-code) | [i] | ||
| 4 | Linear OA(2589, 704, F25, 34) (dual of [704, 615, 35]-code) | [i] | ||
| 5 | Linear OA(2593, 760, F25, 34) (dual of [760, 667, 35]-code) | [i] | ||
| 6 | Linear OA(2594, 762, F25, 34) (dual of [762, 668, 35]-code) | [i] | ||
| 7 | Linear OOA(2566, 317, F25, 2, 34) (dual of [(317, 2), 568, 35]-NRT-code) | [i] | OOA Folding | |