Information on Result #3178451
Digital (22, 42, 1639)-net over F128, using 1 times m-reduction based on digital (22, 43, 1639)-net over F128, using
- net defined by OOA [i] based on linear OOA(12843, 1639, F128, 21, 21) (dual of [(1639, 21), 34376, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12843, 16391, F128, 21) (dual of [16391, 16348, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12843, 16392, F128, 21) (dual of [16392, 16349, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(12843, 16392, F128, 21) (dual of [16392, 16349, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12843, 16391, F128, 21) (dual of [16391, 16348, 22]-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 | (29, 49, 1639)-net in base 64 | [i] | Base Change | |