Information on Result #1711368
Digital (138, 167, 410)-net over F2, using net defined by OOA based on linear OOA(2167, 410, F2, 35, 29) (dual of [(410, 35), 14183, 30]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2167, 821, F2, 7, 29) (dual of [(821, 7), 5580, 30]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2167, 821, F2, 2, 29) (dual of [(821, 2), 1475, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2167, 1046, F2, 2, 29) (dual of [(1046, 2), 1925, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2167, 2092, F2, 29) (dual of [2092, 1925, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2167, 2093, F2, 29) (dual of [2093, 1926, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(2155, 2048, F2, 29) (dual of [2048, 1893, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on 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
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2167, 2093, F2, 29) (dual of [2093, 1926, 30]-code), using
- OOA 2-folding [i] based on linear OA(2167, 2092, F2, 29) (dual of [2092, 1925, 30]-code), using
- discarding factors / shortening the dual code based on linear OOA(2167, 1046, F2, 2, 29) (dual of [(1046, 2), 1925, 30]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2167, 821, F2, 2, 29) (dual of [(821, 2), 1475, 30]-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.