Information on Result #1709044
Digital (68, 82, 743)-net over F2, using net defined by OOA based on linear OOA(282, 743, F2, 21, 14) (dual of [(743, 21), 15521, 15]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(282, 744, F2, 7, 14) (dual of [(744, 7), 5126, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(282, 744, F2, 2, 14) (dual of [(744, 2), 1406, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(282, 1031, F2, 2, 14) (dual of [(1031, 2), 1980, 15]-NRT-code), using
- 21 times duplication [i] based on linear OOA(281, 1031, F2, 2, 14) (dual of [(1031, 2), 1981, 15]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(279, 1030, F2, 2, 14) (dual of [(1030, 2), 1981, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(279, 2060, F2, 14) (dual of [2060, 1981, 15]-code), using
- strength reduction [i] based on linear OA(279, 2060, F2, 15) (dual of [2060, 1981, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(267, 2048, F2, 13) (dual of [2048, 1981, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- strength reduction [i] based on linear OA(279, 2060, F2, 15) (dual of [2060, 1981, 16]-code), using
- OOA 2-folding [i] based on linear OA(279, 2060, F2, 14) (dual of [2060, 1981, 15]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(279, 1030, F2, 2, 14) (dual of [(1030, 2), 1981, 15]-NRT-code), using
- 21 times duplication [i] based on linear OOA(281, 1031, F2, 2, 14) (dual of [(1031, 2), 1981, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(282, 1031, F2, 2, 14) (dual of [(1031, 2), 1980, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(282, 744, F2, 2, 14) (dual of [(744, 2), 1406, 15]-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.