Information on Result #1760005
Digital (216, 257, 1519)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2257, 1519, F2, 2, 41) (dual of [(1519, 2), 2781, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2257, 2074, F2, 2, 41) (dual of [(2074, 2), 3891, 42]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2253, 2072, F2, 2, 41) (dual of [(2072, 2), 3891, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2253, 4144, F2, 41) (dual of [4144, 3891, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2241, 4096, F2, 41) (dual of [4096, 3855, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- OOA 2-folding [i] based on linear OA(2253, 4144, F2, 41) (dual of [4144, 3891, 42]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2253, 2072, F2, 2, 41) (dual of [(2072, 2), 3891, 42]-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.