Information on Result #728689
Linear OA(3264, 1030, F32, 32) (dual of [1030, 966, 33]-code), using construction XX applied to C1 = C([1021,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([1021,29]) based on
- linear OA(3261, 1023, F32, 31) (dual of [1023, 962, 32]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3259, 1023, F32, 30) (dual of [1023, 964, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3263, 1023, F32, 32) (dual of [1023, 960, 33]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,29}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3257, 1023, F32, 29) (dual of [1023, 966, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), 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(8107, 1030, S8, 32) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1680, 1030, S16, 32) | [i] | ||
| 3 | Linear OA(3287, 1128, F32, 32) (dual of [1128, 1041, 33]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(3291, 1150, F32, 32) (dual of [1150, 1059, 33]-code) | [i] | ||
| 5 | Linear OOA(3264, 549, F32, 2, 32) (dual of [(549, 2), 1034, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (32, 64, 549)-net over F32 | [i] | ||
| 7 | Linear OOA(3264, 515, F32, 2, 32) (dual of [(515, 2), 966, 33]-NRT-code) | [i] | OOA Folding | |