Information on Result #1711532
Digital (163, 193, 716)-net over F2, using net defined by OOA based on linear OOA(2193, 716, F2, 40, 30) (dual of [(716, 40), 28447, 31]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2193, 1433, F2, 8, 30) (dual of [(1433, 8), 11271, 31]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2193, 1433, F2, 2, 30) (dual of [(1433, 2), 2673, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2193, 2072, F2, 2, 30) (dual of [(2072, 2), 3951, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2193, 4144, F2, 30) (dual of [4144, 3951, 31]-code), using
- strength reduction [i] based on linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(30) ⊂ Ce(24) [i] based on
- strength reduction [i] based on linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-code), using
- OOA 2-folding [i] based on linear OA(2193, 4144, F2, 30) (dual of [4144, 3951, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2193, 2072, F2, 2, 30) (dual of [(2072, 2), 3951, 31]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2193, 1433, F2, 2, 30) (dual of [(1433, 2), 2673, 31]-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.