Information on Result #1217225
Digital (74, 82, 6585798)-net over F9, using (u, u+v)-construction based on
- digital (20, 24, 2391498)-net over F9, using
- net defined by OOA [i] based on linear OOA(924, 2391498, F9, 4, 4) (dual of [(2391498, 4), 9565968, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(924, 2391498, F9, 3, 4) (dual of [(2391498, 3), 7174470, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(92, 10, F9, 3, 2) (dual of [(10, 3), 28, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;28,9) [i]
- linear OOA(922, 2391488, F9, 3, 4) (dual of [(2391488, 3), 7174442, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(922, 4782976, F9, 4) (dual of [4782976, 4782954, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(922, 4782969, F9, 4) (dual of [4782969, 4782947, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(915, 4782969, F9, 3) (dual of [4782969, 4782954, 4]-code or 4782969-cap in PG(14,9)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 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(922, 4782976, F9, 4) (dual of [4782976, 4782954, 5]-code), using
- linear OOA(92, 10, F9, 3, 2) (dual of [(10, 3), 28, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(924, 2391498, F9, 3, 4) (dual of [(2391498, 3), 7174470, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(924, 2391498, F9, 4, 4) (dual of [(2391498, 4), 9565968, 5]-NRT-code), using
- digital (50, 58, 4194300)-net over F9, using
- net defined by OOA [i] based on linear OOA(958, 4194300, F9, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(958, 8388601, F9, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(958, 8388602, F9, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- trace code [i] based on linear OOA(8129, 4194301, F81, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8129, 8388602, F81, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(8129, 8388602, F81, 8) (dual of [8388602, 8388573, 9]-code), using
- trace code [i] based on linear OOA(8129, 4194301, F81, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(958, 8388602, F9, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(958, 8388601, F9, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(958, 4194300, F9, 10, 8) (dual of [(4194300, 10), 41942942, 9]-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.