Information on Result #1160044
Linear OOA(2243, 1198377, F2, 7, 21) (dual of [(1198377, 7), 8388396, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(212, 6, F2, 7, 10) (dual of [(6, 7), 30, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(7;F,31P) [i] based on function field F/F2 with g(F) = 2 and N(F) ≥ 6, using
- linear OOA(2231, 1198371, F2, 7, 21) (dual of [(1198371, 7), 8388366, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2231, 8388597, F2, 21) (dual of [8388597, 8388366, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2231, large, F2, 21) (dual of [large, large−231, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2231, large, F2, 21) (dual of [large, large−231, 22]-code), using
- OOA 7-folding [i] based on linear OA(2231, 8388597, F2, 21) (dual of [8388597, 8388366, 22]-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(2243, 1198377, F2, 8, 21) (dual of [(1198377, 8), 9586773, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (222, 243, 1198377)-net over F2 | [i] | ||