Information on Result #1095295
Linear OOA(2134, 838865, F2, 5, 13) (dual of [(838865, 5), 4194191, 14]-NRT-code), using OOA 5-folding based on linear OA(2134, 4194325, F2, 13) (dual of [4194325, 4194191, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2134, 4194327, F2, 13) (dual of [4194327, 4194193, 14]-code), using
- construction X 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(21, 23, F2, 1) (dual of [23, 22, 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 X 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(2134, 838865, F2, 5, 12) (dual of [(838865, 5), 4194191, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2135, 838865, F2, 5, 13) (dual of [(838865, 5), 4194190, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2134, 838865, F2, 6, 13) (dual of [(838865, 6), 5033056, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2134, 838865, F2, 7, 13) (dual of [(838865, 7), 5871921, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(2134, 838865, F2, 8, 13) (dual of [(838865, 8), 6710786, 14]-NRT-code) | [i] | ||
| 6 | Digital (121, 134, 838865)-net over F2 | [i] | ||