Information on Result #1228053
Digital (48, 56, large)-net over F128, using (u, u+v)-construction based on
- digital (9, 13, 4194301)-net over F128, using
- net defined by OOA [i] based on linear OOA(12813, 4194301, F128, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12813, 8388602, F128, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12813, large, F128, 4) (dual of [large, large−13, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(12813, large, F128, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12813, 8388602, F128, 4) (dual of [8388602, 8388589, 5]-code), using
- net defined by OOA [i] based on linear OOA(12813, 4194301, F128, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- digital (35, 43, 4194303)-net over F128, using
- net defined by OOA [i] based on linear OOA(12843, 4194303, F128, 12, 8) (dual of [(4194303, 12), 50331593, 9]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(12843, 4194304, F128, 4, 8) (dual of [(4194304, 4), 16777173, 9]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(1284, 1048577, F128, 4, 2) (dual of [(1048577, 4), 4194304, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- Hamming code H(4,128) [i]
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
- linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- 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(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- linear OOA(12829, 2097150, F128, 4, 8) (dual of [(2097150, 4), 8388571, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12829, 8388600, F128, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- OOA 4-folding [i] based on linear OA(12829, 8388600, F128, 8) (dual of [8388600, 8388571, 9]-code), using
- linear OOA(1284, 1048577, F128, 4, 2) (dual of [(1048577, 4), 4194304, 3]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(12843, 4194304, F128, 4, 8) (dual of [(4194304, 4), 16777173, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12843, 4194303, F128, 12, 8) (dual of [(4194303, 12), 50331593, 9]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (49, 56, large)-net over F128 | [i] | t-Expansion | |
| 2 | Digital (49, 57, large)-net over F128 | [i] | Net Duplication | |
| 3 | Digital (48, 55, large)-net over F128 | [i] | m-Reduction | |
| 4 | Digital (48, 54, large)-net over F128 | [i] | ||
| 5 | Digital (48, 53, large)-net over F128 | [i] | ||
| 6 | Digital (48, 52, large)-net over F128 | [i] | ||
| 7 | Digital (48, 51, large)-net over F128 | [i] | ||