Information on Result #1701820
Linear OOA(2194, 1398105, F2, 8, 17) (dual of [(1398105, 8), 11184646, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2194, 1398105, F2, 6, 17) (dual of [(1398105, 6), 8388436, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(29, 5, F2, 6, 8) (dual of [(5, 6), 21, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,21P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- linear OOA(2185, 1398100, F2, 6, 17) (dual of [(1398100, 6), 8388415, 18]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(29, 5, F2, 6, 8) (dual of [(5, 6), 21, 9]-NRT-code), using
Mode: 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(2194, 1398104, F2, 24, 17) (dual of [(1398104, 24), 33554302, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |