Information on Result #724899
Linear OA(2588, 634, F25, 45) (dual of [634, 546, 46]-code), using construction XX applied to C1 = C([621,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([621,41]) based on
- 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 = {−3,−2,…,40}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2586, 624, F25, 45) (dual of [624, 538, 46]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,41}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), 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(2588, 317, F25, 2, 45) (dual of [(317, 2), 546, 46]-NRT-code) | [i] | OOA Folding | |