Information on Result #729084
Linear OA(32103, 1064, F32, 47) (dual of [1064, 961, 48]-code), using construction XX applied to C1 = C([1013,32]), C2 = C([1,36]), C3 = C1 + C2 = C([1,32]), and C∩ = C1 ∩ C2 = C([1013,36]) based on
- linear OA(3283, 1023, F32, 43) (dual of [1023, 940, 44]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−10,−9,…,32}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3269, 1023, F32, 36) (dual of [1023, 954, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3290, 1023, F32, 47) (dual of [1023, 933, 48]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−10,−9,…,36}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3262, 1023, F32, 32) (dual of [1023, 961, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3210, 31, F32, 10) (dual of [31, 21, 11]-code or 31-arc in PG(9,32)), using
- discarding factors / shortening the dual code based on linear OA(3210, 32, F32, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,32)), using
- Reed–Solomon code RS(22,32) [i]
- discarding factors / shortening the dual code based on linear OA(3210, 32, F32, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,32)), using
- linear OA(323, 10, F32, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,32) or 10-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
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 | OA(16129, 1064, S16, 47) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(32103, 532, F32, 2, 47) (dual of [(532, 2), 961, 48]-NRT-code) | [i] | OOA Folding | |