Information on Result #1689685
Linear OOA(2257, 2883582, F2, 7, 17) (dual of [(2883582, 7), 20184817, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2257, 2883582, F2, 3, 17) (dual of [(2883582, 3), 8650489, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(272, 87381, F2, 3, 8) (dual of [(87381, 3), 262071, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(272, 262143, F2, 8) (dual of [262143, 262071, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(272, 262144, F2, 8) (dual of [262144, 262072, 9]-code), using
- 1 times truncation [i] based on linear OA(273, 262145, F2, 9) (dual of [262145, 262072, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(273, 262145, F2, 9) (dual of [262145, 262072, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(272, 262144, F2, 8) (dual of [262144, 262072, 9]-code), using
- OOA 3-folding [i] based on linear OA(272, 262143, F2, 8) (dual of [262143, 262071, 9]-code), using
- linear OOA(2185, 2796201, F2, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- linear OOA(272, 87381, F2, 3, 8) (dual of [(87381, 3), 262071, 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.