Information on Result #1213288
Digital (89, 98, 4195865)-net over F5, using (u, u+v)-construction based on
- digital (12, 16, 1565)-net over F5, using
- net defined by OOA [i] based on linear OOA(516, 1565, F5, 4, 4) (dual of [(1565, 4), 6244, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(516, 1565, F5, 3, 4) (dual of [(1565, 3), 4679, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(516, 3130, F5, 4) (dual of [3130, 3114, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(516, 3125, F5, 4) (dual of [3125, 3109, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(511, 3125, F5, 3) (dual of [3125, 3114, 4]-code or 3125-cap in PG(10,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OA 2-folding and stacking [i] based on linear OA(516, 3130, F5, 4) (dual of [3130, 3114, 5]-code), using
- appending kth column [i] based on linear OOA(516, 1565, F5, 3, 4) (dual of [(1565, 3), 4679, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(516, 1565, F5, 4, 4) (dual of [(1565, 4), 6244, 5]-NRT-code), using
- digital (73, 82, 4194300)-net over F5, using
- net defined by OOA [i] based on linear OOA(582, 4194300, F5, 10, 9) (dual of [(4194300, 10), 41942918, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(582, 8388601, F5, 2, 9) (dual of [(8388601, 2), 16777120, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(582, 8388602, F5, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
- trace code [i] based on linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- trace code [i] based on linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(582, 8388602, F5, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(582, 8388601, F5, 2, 9) (dual of [(8388601, 2), 16777120, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(582, 4194300, F5, 10, 9) (dual of [(4194300, 10), 41942918, 10]-NRT-code), 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.