Information on Result #729243
Linear OA(3297, 1036, F32, 49) (dual of [1036, 939, 50]-code), using construction XX applied to C1 = C([1019,43]), C2 = C([0,44]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C([1019,44]) based on
- linear OA(3292, 1023, F32, 48) (dual of [1023, 931, 49]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−4,−3,…,43}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(3286, 1023, F32, 45) (dual of [1023, 937, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3294, 1023, F32, 49) (dual of [1023, 929, 50]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(3284, 1023, F32, 44) (dual of [1023, 939, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [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 | OA(16122, 1036, S16, 49) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3297, 518, F32, 2, 49) (dual of [(518, 2), 939, 50]-NRT-code) | [i] | OOA Folding | |