Information on Result #1143853
Linear OOA(2221, 1398108, F2, 6, 19) (dual of [(1398108, 6), 8388427, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(213, 8, F2, 6, 9) (dual of [(8, 6), 35, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,38P) [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
- linear OOA(2208, 1398100, F2, 6, 19) (dual of [(1398100, 6), 8388392, 20]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 6-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-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(2221, 1308609, F2, 7, 19) (dual of [(1308609, 7), 9160042, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2221, 1308609, F2, 8, 19) (dual of [(1308609, 8), 10468651, 20]-NRT-code) | [i] | ||
| 3 | Digital (202, 221, 1308609)-net over F2 | [i] | ||