Information on Result #725005
Linear OA(25110, 644, F25, 56) (dual of [644, 534, 57]-code), using construction XX applied to C1 = C([622,52]), C2 = C([6,53]), C3 = C1 + C2 = C([6,52]), and C∩ = C1 ∩ C2 = C([622,53]) based on
- linear OA(25101, 624, F25, 55) (dual of [624, 523, 56]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [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(25103, 624, F25, 56) (dual of [624, 521, 57]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,53}, and designed minimum distance d ≥ |I|+1 = 57 [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(257, 18, F25, 7) (dual of [18, 11, 8]-code or 18-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), 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(25110, 322, F25, 2, 56) (dual of [(322, 2), 534, 57]-NRT-code) | [i] | OOA Folding | |