Information on Result #1228126
Digital (43, 54, 2726297)-net over F128, using (u, u+v)-construction based on
- digital (8, 13, 1048577)-net over F128, using
- net defined by OOA [i] based on linear OOA(12813, 1048577, F128, 5, 5) (dual of [(1048577, 5), 5242872, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(12813, 1048577, F128, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- appending kth column [i] based on linear OOA(12813, 1048577, F128, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12813, 1048577, F128, 5, 5) (dual of [(1048577, 5), 5242872, 6]-NRT-code), using
- digital (30, 41, 1677720)-net over F128, using
- net defined by OOA [i] based on linear OOA(12841, 1677720, F128, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12841, 8388601, F128, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, 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(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12841, 8388601, F128, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(12841, 1677720, F128, 11, 11) (dual of [(1677720, 11), 18454879, 12]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (59, 70, 4839833)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (60, 71, 5452594)-net over F128 | [i] | ||