Information on Result #1115751
Linear OOA(2171, 1677727, F2, 5, 14) (dual of [(1677727, 5), 8388464, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(210, 7, F2, 5, 7) (dual of [(7, 5), 25, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(5;F,27P) [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
- linear OOA(2161, 1677720, F2, 5, 14) (dual of [(1677720, 5), 8388439, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OOA 5-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2236, 3355454, F2, 5, 14) (dual of [(3355454, 5), 16777034, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2171, 1677727, F2, 6, 14) (dual of [(1677727, 6), 10066191, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2171, 1677727, F2, 7, 14) (dual of [(1677727, 7), 11743918, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2171, 1677727, F2, 8, 14) (dual of [(1677727, 8), 13421645, 15]-NRT-code) | [i] | ||
| 5 | Digital (157, 171, 1677727)-net over F2 | [i] | ||