Information on Result #1175425
Linear OOA(2145, 1398105, F2, 8, 12) (dual of [(1398105, 8), 11184695, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(27, 5, F2, 8, 6) (dual of [(5, 8), 33, 7]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(27, 5, F2, 6, 6) (dual of [(5, 6), 23, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(27, 5, F2, 5, 6) (dual of [(5, 5), 18, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(5;F,18P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- appending kth column [i] based on linear OOA(27, 5, F2, 5, 6) (dual of [(5, 5), 18, 7]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(27, 5, F2, 6, 6) (dual of [(5, 6), 23, 7]-NRT-code), using
- linear OOA(2138, 1398100, F2, 8, 12) (dual of [(1398100, 8), 11184662, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-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(2209, 2796210, F2, 8, 12) (dual of [(2796210, 8), 22369471, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |