Information on Result #727527
Linear OA(32100, 354, F32, 53) (dual of [354, 254, 54]-code), using construction XX applied to C1 = C([337,47]), C2 = C([0,48]), C3 = C1 + C2 = C([0,47]), and C∩ = C1 ∩ C2 = C([337,48]) based on
- linear OA(3295, 341, F32, 52) (dual of [341, 246, 53]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {−4,−3,…,47}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3289, 341, F32, 49) (dual of [341, 252, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3297, 341, F32, 53) (dual of [341, 244, 54]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {−4,−3,…,48}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3287, 341, F32, 48) (dual of [341, 254, 49]-code), using the expurgated narrow-sense BCH-code C(I) with length 341 | 322−1, defining interval I = [0,47], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 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(32100, 177, F32, 2, 53) (dual of [(177, 2), 254, 54]-NRT-code) | [i] | OOA Folding | |