Information on Result #724518
Linear OA(2573, 637, F25, 37) (dual of [637, 564, 38]-code), using construction XX applied to C1 = C([620,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([620,32]) based on
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,31}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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 OA(2595, 703, F25, 37) (dual of [703, 608, 38]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2596, 705, F25, 37) (dual of [705, 609, 38]-code) | [i] | ||