Information on Result #1228334
Digital (50, 68, 233403)-net over F128, using (u, u+v)-construction based on
- digital (7, 16, 386)-net over F128, using
- net defined by OOA [i] based on linear OOA(12816, 386, F128, 12, 9) (dual of [(386, 12), 4616, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(12816, 387, F128, 4, 9) (dual of [(387, 4), 1532, 10]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(1283, 129, F128, 4, 3) (dual of [(129, 4), 513, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;513,128) [i]
- linear OOA(1284, 129, F128, 4, 4) (dual of [(129, 4), 512, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;512,128) [i]
- linear OOA(1289, 129, F128, 4, 9) (dual of [(129, 4), 507, 10]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;507,128) [i]
- linear OOA(1283, 129, F128, 4, 3) (dual of [(129, 4), 513, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(12816, 387, F128, 4, 9) (dual of [(387, 4), 1532, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12816, 386, F128, 12, 9) (dual of [(386, 12), 4616, 10]-NRT-code), using
- digital (34, 52, 233017)-net over F128, using
- net defined by OOA [i] based on linear OOA(12852, 233017, F128, 18, 18) (dual of [(233017, 18), 4194254, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12852, 2097153, F128, 18) (dual of [2097153, 2097101, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(12852, 2097153, F128, 18) (dual of [2097153, 2097101, 19]-code), using
- net defined by OOA [i] based on linear OOA(12852, 233017, F128, 18, 18) (dual of [(233017, 18), 4194254, 19]-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.