Information on Result #1213444
Digital (111, 122, 3357242)-net over F5, using (u, u+v)-construction based on
- digital (15, 20, 1802)-net over F5, using
- net defined by OOA [i] based on linear OOA(520, 1802, F5, 6, 5) (dual of [(1802, 6), 10792, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(520, 1803, F5, 2, 5) (dual of [(1803, 2), 3586, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(51, 601, F5, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(51, s, F5, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(51, s, F5, 2, 1) for arbitrarily large s, using
- linear OOA(55, 601, F5, 2, 2) (dual of [(601, 2), 1197, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(55, 781, F5, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
- appending kth column [i] based on linear OA(55, 781, F5, 2) (dual of [781, 776, 3]-code), using
- Hamming code H(5,5) [i]
- appending kth column [i] based on linear OA(55, 781, F5, 2) (dual of [781, 776, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(55, 781, F5, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
- linear OOA(514, 601, F5, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- trace code [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- OOA 2-folding [i] based on linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- linear OOA(51, 601, F5, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(520, 1803, F5, 2, 5) (dual of [(1803, 2), 3586, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(520, 1802, F5, 6, 5) (dual of [(1802, 6), 10792, 6]-NRT-code), using
- digital (91, 102, 3355440)-net over F5, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2551, large, F25, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2551, 8388601, F25, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2551, 1677720, F25, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F25, using
Mode: Constructive and 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.