Information on Result #1051411
Linear OOA(2134, 1048582, F2, 4, 12) (dual of [(1048582, 4), 4194194, 13]-NRT-code), using OOA 4-folding based on linear OA(2134, 4194328, F2, 12) (dual of [4194328, 4194194, 13]-code), using
- strength reduction [i] based on linear OA(2134, 4194328, F2, 13) (dual of [4194328, 4194194, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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(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(12) ⊂ Ce(10) [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(2135, 1048582, F2, 4, 12) (dual of [(1048582, 4), 4194193, 13]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2136, 1048582, F2, 4, 12) (dual of [(1048582, 4), 4194192, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2137, 1048582, F2, 4, 12) (dual of [(1048582, 4), 4194191, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(2134, 1048582, F2, 5, 12) (dual of [(1048582, 5), 5242776, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2134, 1048582, F2, 6, 12) (dual of [(1048582, 6), 6291358, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(2134, 1048582, F2, 7, 12) (dual of [(1048582, 7), 7339940, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(2134, 1048582, F2, 8, 12) (dual of [(1048582, 8), 8388522, 13]-NRT-code) | [i] | ||
| 8 | Digital (122, 134, 1048582)-net over F2 | [i] | ||