Information on Result #870578
Linear OOA(3263, 513, F32, 2, 32) (dual of [(513, 2), 963, 33]-NRT-code), using OOA 2-folding based on linear OA(3263, 1026, F32, 32) (dual of [1026, 963, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3263, 1027, F32, 32) (dual of [1027, 964, 33]-code), using
- construction XX applied to C1 = C([1022,29]), C2 = C([0,30]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([1022,30]) [i] 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 = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3261, 1023, F32, 31) (dual of [1023, 962, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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 = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [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(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
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,29]), C2 = C([0,30]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([1022,30]) [i] based on
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(3280, 557, F32, 2, 32) (dual of [(557, 2), 1034, 33]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3282, 577, F32, 2, 32) (dual of [(577, 2), 1072, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3284, 589, F32, 2, 32) (dual of [(589, 2), 1094, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3286, 611, F32, 2, 32) (dual of [(611, 2), 1136, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(3288, 617, F32, 2, 32) (dual of [(617, 2), 1146, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(3290, 633, F32, 2, 32) (dual of [(633, 2), 1176, 33]-NRT-code) | [i] | ||
| 7 | Digital (31, 63, 513)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |