Information on Result #700115
Linear OA(12869, 16416, F128, 30) (dual of [16416, 16347, 31]-code), using construction X applied to Ce(29) ⊂ Ce(18) based on
- linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12810, 32, F128, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,128)), using
- discarding factors / shortening the dual code based on linear OA(12810, 128, F128, 10) (dual of [128, 118, 11]-code or 128-arc in PG(9,128)), using
- Reed–Solomon code RS(118,128) [i]
- discarding factors / shortening the dual code based on linear OA(12810, 128, F128, 10) (dual of [128, 118, 11]-code or 128-arc in PG(9,128)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OA(6481, 16416, S64, 30) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12869, 11647, F128, 2, 30) (dual of [(11647, 2), 23225, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12869, 11647, F128, 3, 30) (dual of [(11647, 3), 34872, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(12869, 11647, F128, 4, 30) (dual of [(11647, 4), 46519, 31]-NRT-code) | [i] | ||
| 5 | Digital (39, 69, 11647)-net over F128 | [i] | ||
| 6 | Linear OOA(12869, 8208, F128, 2, 30) (dual of [(8208, 2), 16347, 31]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12869, 5472, F128, 3, 30) (dual of [(5472, 3), 16347, 31]-NRT-code) | [i] | ||
| 8 | Linear OOA(12869, 4104, F128, 4, 30) (dual of [(4104, 4), 16347, 31]-NRT-code) | [i] | ||