Information on Result #870795
Linear OOA(3268, 515, F32, 2, 35) (dual of [(515, 2), 962, 36]-NRT-code), using OOA 2-folding based on linear OA(3268, 1030, F32, 35) (dual of [1030, 962, 36]-code), using
- construction XX applied to C1 = C([0,33]), C2 = C([3,34]), C3 = C1 + C2 = C([3,33]), and C∩ = C1 ∩ C2 = C([0,34]) [i] based on
- linear OA(3264, 1023, F32, 34) (dual of [1023, 959, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [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 = {3,4,…,34}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3266, 1023, F32, 35) (dual of [1023, 957, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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 = {3,4,…,33}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(322, 5, F32, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), 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 | Linear OOA(3296, 635, F32, 2, 35) (dual of [(635, 2), 1174, 36]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Digital (33, 68, 509)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |