Information on Result #869803
Linear OOA(3244, 515, F32, 2, 22) (dual of [(515, 2), 986, 23]-NRT-code), using OOA 2-folding based on linear OA(3244, 1030, F32, 22) (dual of [1030, 986, 23]-code), using
- construction XX applied to C1 = C([1021,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1021,19]) [i] based on
- linear OA(3241, 1023, F32, 21) (dual of [1023, 982, 22]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3243, 1023, F32, 22) (dual of [1023, 980, 23]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,19}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3237, 1023, F32, 19) (dual of [1023, 986, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(3256, 559, F32, 2, 22) (dual of [(559, 2), 1062, 23]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3258, 579, F32, 2, 22) (dual of [(579, 2), 1100, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3260, 591, F32, 2, 22) (dual of [(591, 2), 1122, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(3262, 613, F32, 2, 22) (dual of [(613, 2), 1164, 23]-NRT-code) | [i] | ||
| 5 | Digital (22, 44, 515)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |