Information on Result #1217262
Digital (80, 89, 6585792)-net over F9, using (u, u+v)-construction based on
- digital (19, 23, 2391492)-net over F9, using
- net defined by OOA [i] based on linear OOA(923, 2391492, F9, 4, 4) (dual of [(2391492, 4), 9565945, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(923, 2391492, F9, 3, 4) (dual of [(2391492, 3), 7174453, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(923, 4782984, F9, 4) (dual of [4782984, 4782961, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [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(98, 4782969, F9, 2) (dual of [4782969, 4782961, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(923, 4782984, F9, 4) (dual of [4782984, 4782961, 5]-code), using
- appending kth column [i] based on linear OOA(923, 2391492, F9, 3, 4) (dual of [(2391492, 3), 7174453, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(923, 2391492, F9, 4, 4) (dual of [(2391492, 4), 9565945, 5]-NRT-code), using
- digital (57, 66, 4194300)-net over F9, using
- net defined by OOA [i] based on linear OOA(966, 4194300, F9, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(966, 8388601, F9, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, 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(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(966, 8388601, F9, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(966, 4194300, F9, 10, 9) (dual of [(4194300, 10), 41942934, 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.