Information on Result #1096669
Linear OOA(2189, 3283, F2, 5, 27) (dual of [(3283, 5), 16226, 28]-NRT-code), using OOA 5-folding based on linear OA(2189, 16415, F2, 27) (dual of [16415, 16226, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2189, 16416, F2, 27) (dual of [16416, 16227, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- 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(2155, 16384, F2, 23) (dual of [16384, 16229, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(26) ⊂ Ce(22) [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(2189, 3283, F2, 5, 26) (dual of [(3283, 5), 16226, 27]-NRT-code) | [i] | Strength Reduction for OOAs | |
2 | Linear OOA(2190, 3283, F2, 5, 27) (dual of [(3283, 5), 16225, 28]-NRT-code) | [i] | OOA Duplication | |
3 | Linear OOA(2189, 3283, F2, 6, 27) (dual of [(3283, 6), 19509, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
4 | Linear OOA(2189, 3283, F2, 7, 27) (dual of [(3283, 7), 22792, 28]-NRT-code) | [i] | ||
5 | Linear OOA(2189, 3283, F2, 8, 27) (dual of [(3283, 8), 26075, 28]-NRT-code) | [i] | ||
6 | Digital (162, 189, 3283)-net over F2 | [i] |