Information on Result #700093
Linear OA(12861, 16410, F128, 27) (dual of [16410, 16349, 28]-code), using construction X applied to Ce(26) ⊂ Ce(17) based on
- linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1288, 26, F128, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,128)), using
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- Reed–Solomon code RS(120,128) [i]
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), 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 | Linear OOA(12861, 9132, F128, 2, 27) (dual of [(9132, 2), 18203, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12861, 9132, F128, 3, 27) (dual of [(9132, 3), 27335, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(12861, 9132, F128, 4, 27) (dual of [(9132, 4), 36467, 28]-NRT-code) | [i] | ||
| 4 | Digital (34, 61, 9132)-net over F128 | [i] | ||
| 5 | Linear OOA(12861, 8205, F128, 2, 27) (dual of [(8205, 2), 16349, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12861, 5470, F128, 3, 27) (dual of [(5470, 3), 16349, 28]-NRT-code) | [i] | ||