Information on Result #724931
Linear OA(25102, 646, F25, 50) (dual of [646, 544, 51]-code), using construction XX applied to C1 = C([617,41]), C2 = C([0,42]), C3 = C1 + C2 = C([0,41]), and C∩ = C1 ∩ C2 = C([617,42]) 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 = {−7,−6,…,41}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2582, 624, F25, 43) (dual of [624, 542, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [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 = {−7,−6,…,42}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(256, 20, F25, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), 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(25102, 323, F25, 2, 50) (dual of [(323, 2), 544, 51]-NRT-code) | [i] | OOA Folding | |