Information on Result #1131712
Linear OOA(2164, 43694, F2, 6, 19) (dual of [(43694, 6), 262000, 20]-NRT-code), using OOA 6-folding based on linear OA(2164, 262164, F2, 19) (dual of [262164, 262000, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2145, 262144, F2, 17) (dual of [262144, 261999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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
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(2165, 43694, F2, 6, 19) (dual of [(43694, 6), 261999, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2166, 43694, F2, 6, 19) (dual of [(43694, 6), 261998, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(2167, 43694, F2, 6, 19) (dual of [(43694, 6), 261997, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(2168, 43694, F2, 6, 19) (dual of [(43694, 6), 261996, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(2164, 43694, F2, 7, 19) (dual of [(43694, 7), 305694, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2164, 43694, F2, 8, 19) (dual of [(43694, 8), 349388, 20]-NRT-code) | [i] | ||
| 7 | Digital (145, 164, 43694)-net over F2 | [i] | ||