Information on Result #1132075
Linear OOA(2227, 174770, F2, 6, 22) (dual of [(174770, 6), 1048393, 23]-NRT-code), using OOA 6-folding based on linear OA(2227, 1048620, F2, 22) (dual of [1048620, 1048393, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2227, 1048622, F2, 22) (dual of [1048622, 1048395, 23]-code), using
- 1 times truncation [i] based on linear OA(2228, 1048623, F2, 23) (dual of [1048623, 1048395, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 47, F2, 3) (dual of [47, 40, 4]-code or 47-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
- 1 times truncation [i] based on linear OA(2228, 1048623, F2, 23) (dual of [1048623, 1048395, 24]-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(2229, 174770, F2, 6, 22) (dual of [(174770, 6), 1048391, 23]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2227, 174770, F2, 7, 22) (dual of [(174770, 7), 1223163, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2227, 174770, F2, 8, 22) (dual of [(174770, 8), 1397933, 23]-NRT-code) | [i] | ||
| 4 | Digital (205, 227, 174770)-net over F2 | [i] | ||