Information on Result #699734
Linear OA(12817, 2097160, F128, 6) (dual of [2097160, 2097143, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 8, F128, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
- dual of repetition code with length 8 [i]
- linear OA(1281, 8, F128, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- Reed–Solomon code RS(127,128) [i]
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), 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(1630, 2097160, S16, 6) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3224, 2097160, S32, 6) | [i] | ||
| 3 | OA(6420, 2097160, S64, 6) | [i] | ||
| 4 | Linear OOA(12817, 2097160, F128, 2, 6) (dual of [(2097160, 2), 4194303, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12817, 2097160, F128, 3, 6) (dual of [(2097160, 3), 6291463, 7]-NRT-code) | [i] | ||
| 6 | Linear OOA(12817, 2097160, F128, 4, 6) (dual of [(2097160, 4), 8388623, 7]-NRT-code) | [i] | ||
| 7 | Digital (11, 17, 2097160)-net over F128 | [i] | ||
| 8 | Linear OOA(12817, 1048580, F128, 2, 6) (dual of [(1048580, 2), 2097143, 7]-NRT-code) | [i] | OOA Folding | |