Information on Result #700123
Linear OA(12853, 16416, F128, 22) (dual of [16416, 16363, 23]-code), using construction X applied to Ce(21) ⊂ Ce(10) based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(6462, 16416, S64, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12853, 16416, F128, 2, 22) (dual of [(16416, 2), 32779, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12853, 16416, F128, 3, 22) (dual of [(16416, 3), 49195, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(12853, 16416, F128, 4, 22) (dual of [(16416, 4), 65611, 23]-NRT-code) | [i] | ||
| 5 | Digital (31, 53, 16416)-net over F128 | [i] | ||
| 6 | Linear OOA(12853, 8208, F128, 2, 22) (dual of [(8208, 2), 16363, 23]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12853, 5472, F128, 3, 22) (dual of [(5472, 3), 16363, 23]-NRT-code) | [i] | ||
| 8 | Linear OOA(12853, 4104, F128, 4, 22) (dual of [(4104, 4), 16363, 23]-NRT-code) | [i] | ||