Information on Result #724978
Linear OA(2596, 634, F25, 49) (dual of [634, 538, 50]-code), using construction XX applied to C1 = C([621,44]), C2 = C([0,45]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([621,45]) based on
- linear OA(2592, 624, F25, 48) (dual of [624, 532, 49]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,44}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(2588, 624, F25, 46) (dual of [624, 536, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2594, 624, F25, 49) (dual of [624, 530, 50]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,45}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2586, 624, F25, 45) (dual of [624, 538, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [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(2596, 317, F25, 2, 49) (dual of [(317, 2), 538, 50]-NRT-code) | [i] | OOA Folding | |