Information on Result #1095891
Linear OOA(2151, 13113, F2, 5, 19) (dual of [(13113, 5), 65414, 20]-NRT-code), using OOA 5-folding based on linear OA(2151, 65565, F2, 19) (dual of [65565, 65414, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2151, 65568, F2, 19) (dual of [65568, 65417, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(18) ⊂ Ce(14) [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(2151, 13113, F2, 6, 19) (dual of [(13113, 6), 78527, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2151, 13113, F2, 7, 19) (dual of [(13113, 7), 91640, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(2151, 13113, F2, 8, 19) (dual of [(13113, 8), 104753, 20]-NRT-code) | [i] | ||
| 4 | Digital (132, 151, 13113)-net over F2 | [i] | ||