Information on Result #1711250
Digital (161, 189, 1037)-net over F2, using net defined by OOA based on linear OOA(2189, 1037, F2, 35, 28) (dual of [(1037, 35), 36106, 29]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2189, 2075, F2, 7, 28) (dual of [(2075, 7), 14336, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2189, 2076, F2, 7, 28) (dual of [(2076, 7), 14343, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2189, 2076, F2, 3, 28) (dual of [(2076, 3), 6039, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2189, 2741, F2, 3, 28) (dual of [(2741, 3), 8034, 29]-NRT-code), using
- strength reduction [i] based on linear OOA(2189, 2741, F2, 3, 29) (dual of [(2741, 3), 8034, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2189, 8223, F2, 29) (dual of [8223, 8034, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-code), using
- OOA 3-folding [i] based on linear OA(2189, 8223, F2, 29) (dual of [8223, 8034, 30]-code), using
- strength reduction [i] based on linear OOA(2189, 2741, F2, 3, 29) (dual of [(2741, 3), 8034, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2189, 2741, F2, 3, 28) (dual of [(2741, 3), 8034, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2189, 2076, F2, 3, 28) (dual of [(2076, 3), 6039, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2189, 2076, F2, 7, 28) (dual of [(2076, 7), 14343, 29]-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.