Information on Result #3264126
Digital (62, 84, 5959)-net over F16, using 161 times duplication based on digital (61, 83, 5959)-net over F16, using
- net defined by OOA [i] based on linear OOA(1683, 5959, F16, 22, 22) (dual of [(5959, 22), 131015, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(1683, 65549, F16, 22) (dual of [65549, 65466, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(1683, 65550, F16, 22) (dual of [65550, 65467, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(1683, 65550, F16, 22) (dual of [65550, 65467, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(1683, 65549, F16, 22) (dual of [65549, 65466, 23]-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 | (90, 112, 5959)-net in base 8 | [i] | Base Change | |