Information on Result #724976
Linear OA(2593, 631, F25, 48) (dual of [631, 538, 49]-code), using construction XX applied to C1 = C([622,44]), C2 = C([0,45]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([622,45]) based on
- 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 = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2588, 624, F25, 46) (dual of [624, 536, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [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 = {−2,−1,…,45}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(2586, 624, F25, 45) (dual of [624, 538, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), 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 OA(2597, 645, F25, 48) (dual of [645, 548, 49]-code) | [i] | Varšamov–Edel Lengthening | |