Information on Result #1053572
Linear OOA(2216, 4103, F2, 4, 30) (dual of [(4103, 4), 16196, 31]-NRT-code), using OOA 4-folding based on linear OA(2216, 16412, F2, 30) (dual of [16412, 16196, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 16415, F2, 30) (dual of [16415, 16199, 31]-code), using
- 1 times truncation [i] based on linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), 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(2216, 3597, F2, 5, 30) (dual of [(3597, 5), 17769, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2216, 3597, F2, 6, 30) (dual of [(3597, 6), 21366, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2216, 3597, F2, 7, 30) (dual of [(3597, 7), 24963, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2216, 3597, F2, 8, 30) (dual of [(3597, 8), 28560, 31]-NRT-code) | [i] | ||
| 5 | Digital (186, 216, 3597)-net over F2 | [i] | ||