Information on Result #725002
Linear OA(25104, 638, F25, 54) (dual of [638, 534, 55]-code), using construction XX applied to C1 = C([0,52]), C2 = C([6,53]), C3 = C1 + C2 = C([6,52]), 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(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 = {6,7,…,53}, and designed minimum distance d ≥ |I|+1 = 49 [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(2590, 624, F25, 47) (dual of [624, 534, 48]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {6,7,…,52}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(255, 12, F25, 5) (dual of [12, 7, 6]-code or 12-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), 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(25104, 319, F25, 2, 54) (dual of [(319, 2), 534, 55]-NRT-code) | [i] | OOA Folding | |