Information on Result #862228
Linear OOA(2560, 317, F25, 2, 31) (dual of [(317, 2), 574, 32]-NRT-code), using OOA 2-folding based on linear OA(2560, 634, F25, 31) (dual of [634, 574, 32]-code), using
- construction XX applied to C1 = C([621,26]), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([621,27]) [i] based on
- linear OA(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,26}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2552, 624, F25, 28) (dual of [624, 572, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,27}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2550, 624, F25, 27) (dual of [624, 574, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [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 OOA(2575, 343, F25, 2, 31) (dual of [(343, 2), 611, 32]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2579, 383, F25, 2, 31) (dual of [(383, 2), 687, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2585, 443, F25, 2, 31) (dual of [(443, 2), 801, 32]-NRT-code) | [i] | ||