Information on Result #2788468
Linear OOA(2129, 65541, F2, 4, 14) (dual of [(65541, 4), 262035, 15]-NRT-code), using 21 times duplication based on linear OOA(2128, 65541, F2, 4, 14) (dual of [(65541, 4), 262036, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2128, 262164, F2, 14) (dual of [262164, 262036, 15]-code), using
- strength reduction [i] based on linear OA(2128, 262164, F2, 15) (dual of [262164, 262036, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2127, 262144, F2, 15) (dual of [262144, 262017, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2109, 262144, F2, 13) (dual of [262144, 262035, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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(14) ⊂ Ce(12) [i] based on
- strength reduction [i] based on linear OA(2128, 262164, F2, 15) (dual of [262164, 262036, 16]-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(2129, 62898, F2, 5, 14) (dual of [(62898, 5), 314361, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2129, 62898, F2, 6, 14) (dual of [(62898, 6), 377259, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(2129, 62898, F2, 7, 14) (dual of [(62898, 7), 440157, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2129, 62898, F2, 8, 14) (dual of [(62898, 8), 503055, 15]-NRT-code) | [i] | ||
| 5 | Digital (115, 129, 62898)-net over F2 | [i] | ||