Information on Result #1143813
Linear OOA(2219, 1398107, F2, 6, 18) (dual of [(1398107, 6), 8388423, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(212, 7, F2, 6, 9) (dual of [(7, 6), 30, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,32P) [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
- linear OOA(2207, 1398100, F2, 6, 18) (dual of [(1398100, 6), 8388393, 19]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 6-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-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(2219, 1398107, F2, 7, 18) (dual of [(1398107, 7), 9786530, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2219, 1398107, F2, 8, 18) (dual of [(1398107, 8), 11184637, 19]-NRT-code) | [i] | ||
| 3 | Digital (201, 219, 1398107)-net over F2 | [i] | ||