Information on Result #3267750
Digital (48, 72, 174763)-net over F128, using 1281 times duplication based on digital (47, 71, 174763)-net over F128, using
- net defined by OOA [i] based on linear OOA(12871, 174763, F128, 24, 24) (dual of [(174763, 24), 4194241, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12871, 2097156, F128, 24) (dual of [2097156, 2097085, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12871, 2097159, F128, 24) (dual of [2097159, 2097088, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(12871, 2097159, F128, 24) (dual of [2097159, 2097088, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(12871, 2097156, F128, 24) (dual of [2097156, 2097085, 25]-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 | (102, 126, 174763)-net in base 16 | [i] | Base Change | |
| 2 | (60, 84, 174763)-net in base 64 | [i] | ||