Information on Result #724996
Linear OA(25108, 644, F25, 55) (dual of [644, 536, 56]-code), using construction XX applied to C1 = C([623,52]), C2 = C([7,53]), C3 = C1 + C2 = C([7,52]), and C∩ = C1 ∩ C2 = C([623,53]) based on
- linear OA(2599, 624, F25, 54) (dual of [624, 525, 55]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,52}, 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 = {7,8,…,53}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- 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 = {−1,0,…,53}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2588, 624, F25, 46) (dual of [624, 536, 47]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,52}, and designed minimum distance d ≥ |I|+1 = 47 [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(25108, 322, F25, 2, 55) (dual of [(322, 2), 536, 56]-NRT-code) | [i] | OOA Folding | |