Information on Result #724965
Linear OA(25100, 640, F25, 50) (dual of [640, 540, 51]-code), using construction XX applied to C1 = C([619,43]), C2 = C([0,44]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C([619,44]) based on
- 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 = {−5,−4,…,43}, 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(2596, 624, F25, 50) (dual of [624, 528, 51]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,44}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2584, 624, F25, 44) (dual of [624, 540, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), 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(25100, 320, F25, 2, 50) (dual of [(320, 2), 540, 51]-NRT-code) | [i] | OOA Folding | |