Information on Result #1684818
Linear OOA(2196, 1398107, F2, 7, 17) (dual of [(1398107, 7), 9786553, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2196, 1398107, F2, 6, 17) (dual of [(1398107, 6), 8388446, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(211, 7, F2, 6, 8) (dual of [(7, 6), 31, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,33P) [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, 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(211, 7, F2, 6, 8) (dual of [(7, 6), 31, 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
None.