Information on Result #727580
Linear OA(32107, 351, F32, 58) (dual of [351, 244, 59]-code), using construction XX applied to C1 = C([340,55]), C2 = C([3,56]), C3 = C1 + C2 = C([3,55]), and C∩ = C1 ∩ C2 = C([340,56]) based on
- linear OA(32102, 341, F32, 57) (dual of [341, 239, 58]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {−1,0,…,55}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(3299, 341, F32, 54) (dual of [341, 242, 55]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {3,4,…,56}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(32104, 341, F32, 58) (dual of [341, 237, 59]-code), using the BCH-code C(I) with length 341 | 322−1, defining interval I = {−1,0,…,56}, and designed minimum distance d ≥ |I|+1 = 59 [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 = {3,4,…,55}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(323, 8, F32, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,32) or 8-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(32107, 175, F32, 2, 58) (dual of [(175, 2), 243, 59]-NRT-code) | [i] | OOA Folding | |