Information on Result #1096183
Linear OOA(2184, 13115, F2, 5, 22) (dual of [(13115, 5), 65391, 23]-NRT-code), using OOA 5-folding based on linear OA(2184, 65575, F2, 22) (dual of [65575, 65391, 23]-code), using
- strength reduction [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [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(2185, 13115, F2, 5, 22) (dual of [(13115, 5), 65390, 23]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2186, 13115, F2, 5, 22) (dual of [(13115, 5), 65389, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2184, 13115, F2, 6, 22) (dual of [(13115, 6), 78506, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2184, 13115, F2, 7, 22) (dual of [(13115, 7), 91621, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(2184, 13115, F2, 8, 22) (dual of [(13115, 8), 104736, 23]-NRT-code) | [i] | ||
| 6 | Digital (162, 184, 13115)-net over F2 | [i] | ||