Information on Result #2257604
Linear OA(2136, 4194330, F2, 12) (dual of [4194330, 4194194, 13]-code), using 3 times code embedding in larger space based on linear OA(2133, 4194327, F2, 12) (dual of [4194327, 4194194, 13]-code), using
- 1 times truncation [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(2136, 838866, F2, 5, 12) (dual of [(838866, 5), 4194194, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2136, 699055, F2, 6, 12) (dual of [(699055, 6), 4194194, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2136, 699055, F2, 7, 12) (dual of [(699055, 7), 4893249, 13]-NRT-code) | [i] | OA Folding and Stacking | |
| 4 | Linear OOA(2136, 699055, F2, 8, 12) (dual of [(699055, 8), 5592304, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(2136, 699055, F2, 12, 12) (dual of [(699055, 12), 8388524, 13]-NRT-code) | [i] | ||