Information on Result #870279
Linear OOA(3256, 515, F32, 2, 28) (dual of [(515, 2), 974, 29]-NRT-code), using OOA 2-folding based on linear OA(3256, 1030, F32, 28) (dual of [1030, 974, 29]-code), using
- construction XX applied to C1 = C([1021,24]), C2 = C([0,25]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([1021,25]) [i] based on
- linear OA(3253, 1023, F32, 27) (dual of [1023, 970, 28]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3251, 1023, F32, 26) (dual of [1023, 972, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3255, 1023, F32, 28) (dual of [1023, 968, 29]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,25}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3249, 1023, F32, 25) (dual of [1023, 974, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [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 | Linear OOA(3271, 559, F32, 2, 28) (dual of [(559, 2), 1047, 29]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3273, 579, F32, 2, 28) (dual of [(579, 2), 1085, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3275, 591, F32, 2, 28) (dual of [(591, 2), 1107, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3277, 613, F32, 2, 28) (dual of [(613, 2), 1149, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(3279, 619, F32, 2, 28) (dual of [(619, 2), 1159, 29]-NRT-code) | [i] | ||
| 6 | Digital (28, 56, 515)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |