Information on Result #1708670
Digital (168, 180, 3727814)-net over F2, using net defined by OOA based on linear OOA(2180, 3727814, F2, 18, 12) (dual of [(3727814, 18), 67100472, 13]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2180, 3727815, F2, 6, 12) (dual of [(3727815, 6), 22366710, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2180, 3727815, F2, 2, 12) (dual of [(3727815, 2), 7455450, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 4202493, F2, 2, 12) (dual of [(4202493, 2), 8404806, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2178, 4202492, F2, 2, 12) (dual of [(4202492, 2), 8404806, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(240, 8191, F2, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- 1 times m-reduction [i] based on digital (34, 41, 8191)-net over F2, using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- linear OOA(2138, 4194301, F2, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- linear OOA(240, 8191, F2, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2178, 4202492, F2, 2, 12) (dual of [(4202492, 2), 8404806, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 4202493, F2, 2, 12) (dual of [(4202493, 2), 8404806, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2180, 3727815, F2, 2, 12) (dual of [(3727815, 2), 7455450, 13]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.