Information on Result #734463
Linear OA(3222, 32805, F32, 7) (dual of [32805, 32783, 8]-code), using (u, u+v)-construction based on
- linear OA(323, 34, F32, 3) (dual of [34, 31, 4]-code or 34-arc in PG(2,32) or 34-cap in PG(2,32)), using
- linear OA(3219, 32771, F32, 7) (dual of [32771, 32752, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(3219, 32768, F32, 7) (dual of [32768, 32749, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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
- construction X applied to Ce(6) ⊂ Ce(5) [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(3222, 32805, F32, 2, 7) (dual of [(32805, 2), 65588, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (15, 22, 32805)-net over F32 | [i] | ||
| 3 | Linear OOA(3222, 16402, F32, 2, 7) (dual of [(16402, 2), 32782, 8]-NRT-code) | [i] | OOA Folding | |