Information on Result #1051234
Linear OOA(2112, 1048582, F2, 4, 10) (dual of [(1048582, 4), 4194216, 11]-NRT-code), using OOA 4-folding based on linear OA(2112, 4194328, F2, 10) (dual of [4194328, 4194216, 11]-code), using
- strength reduction [i] based on linear OA(2112, 4194328, F2, 11) (dual of [4194328, 4194216, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(2111, 4194304, F2, 11) (dual of [4194304, 4194193, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(289, 4194304, F2, 9) (dual of [4194304, 4194215, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(10) ⊂ Ce(8) [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(2113, 1048582, F2, 4, 10) (dual of [(1048582, 4), 4194215, 11]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2114, 1048582, F2, 4, 10) (dual of [(1048582, 4), 4194214, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(2112, 1048582, F2, 5, 10) (dual of [(1048582, 5), 5242798, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2112, 1048582, F2, 6, 10) (dual of [(1048582, 6), 6291380, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(2112, 1048582, F2, 7, 10) (dual of [(1048582, 7), 7339962, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(2112, 1048582, F2, 8, 10) (dual of [(1048582, 8), 8388544, 11]-NRT-code) | [i] | ||
| 7 | Digital (102, 112, 1048582)-net over F2 | [i] | ||