Information on Result #724953
Linear OA(25108, 650, F25, 54) (dual of [650, 542, 55]-code), using construction XX applied to C1 = C([0,52]), C2 = C([10,53]), C3 = C1 + C2 = C([10,52]), and C∩ = C1 ∩ C2 = C([0,53]) based on
- linear OA(2597, 624, F25, 53) (dual of [624, 527, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2584, 624, F25, 44) (dual of [624, 540, 45]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,53}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2599, 624, F25, 54) (dual of [624, 525, 55]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,53], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2582, 624, F25, 43) (dual of [624, 542, 44]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,52}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(259, 24, F25, 9) (dual of [24, 15, 10]-code or 24-arc in PG(8,25)), using
- discarding factors / shortening the dual code based on linear OA(259, 25, F25, 9) (dual of [25, 16, 10]-code or 25-arc in PG(8,25)), using
- Reed–Solomon code RS(16,25) [i]
- discarding factors / shortening the dual code based on linear OA(259, 25, F25, 9) (dual of [25, 16, 10]-code or 25-arc in PG(8,25)), 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(25108, 325, F25, 2, 54) (dual of [(325, 2), 542, 55]-NRT-code) | [i] | OOA Folding | |