Information on Result #3267752
Digital (54, 78, 174765)-net over F128, using 1281 times duplication based on digital (53, 77, 174765)-net over F128, using
- net defined by OOA [i] based on linear OOA(12877, 174765, F128, 24, 24) (dual of [(174765, 24), 4194283, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12877, 2097180, F128, 24) (dual of [2097180, 2097103, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12877, 2097183, F128, 24) (dual of [2097183, 2097106, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [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(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(12877, 2097183, F128, 24) (dual of [2097183, 2097106, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(12877, 2097180, F128, 24) (dual of [2097180, 2097103, 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 | (67, 91, 174765)-net in base 64 | [i] | Base Change | |