Information on Result #1813885
Digital (40, 60, 873861)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12860, 873861, F128, 2, 20) (dual of [(873861, 2), 1747662, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12860, 1048581, F128, 2, 20) (dual of [(1048581, 2), 2097102, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12860, 2097162, F128, 20) (dual of [2097162, 2097102, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12860, 2097163, F128, 20) (dual of [2097163, 2097103, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-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(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(12860, 2097163, F128, 20) (dual of [2097163, 2097103, 21]-code), using
- OOA 2-folding [i] based on linear OA(12860, 2097162, F128, 20) (dual of [2097162, 2097102, 21]-code), using
Mode: 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 | (50, 70, 873861)-net in base 64 | [i] | Base Change | |