Information on Result #1846589
(55, 77, 782307)-net in base 64, using base change based on digital (44, 66, 782307)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12866, 782307, F128, 2, 22) (dual of [(782307, 2), 1564548, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12866, 1048581, F128, 2, 22) (dual of [(1048581, 2), 2097096, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12866, 2097162, F128, 22) (dual of [2097162, 2097096, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12866, 2097163, F128, 22) (dual of [2097163, 2097097, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- 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(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(12866, 2097163, F128, 22) (dual of [2097163, 2097097, 23]-code), using
- OOA 2-folding [i] based on linear OA(12866, 2097162, F128, 22) (dual of [2097162, 2097096, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(12866, 1048581, F128, 2, 22) (dual of [(1048581, 2), 2097096, 23]-NRT-code), using
Mode: Arbitrary.
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 | (56, 78, 782307)-net in base 64 | [i] | Net Duplication | |
| 2 | OOA(6477, 782307, S64, 3, 22) | [i] | Extracting Embedded OOA | |