Information on Result #1175669
Linear OOA(2170, 1198376, F2, 8, 15) (dual of [(1198376, 8), 9586838, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(28, 5, F2, 8, 7) (dual of [(5, 8), 32, 8]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(28, 5, F2, 7, 7) (dual of [(5, 7), 27, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(28, 5, F2, 6, 7) (dual of [(5, 6), 22, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,22P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- appending kth column [i] based on linear OOA(28, 5, F2, 6, 7) (dual of [(5, 6), 22, 8]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(28, 5, F2, 7, 7) (dual of [(5, 7), 27, 8]-NRT-code), using
- linear OOA(2162, 1198371, F2, 8, 15) (dual of [(1198371, 8), 9586806, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-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(2235, 2396752, F2, 8, 15) (dual of [(2396752, 8), 19173781, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |