Information on Result #700479
Linear OA(25667, 65574, F256, 28) (dual of [65574, 65507, 29]-code), using construction X applied to Ce(27) ⊂ Ce(14) based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25612, 38, F256, 12) (dual of [38, 26, 13]-code or 38-arc in PG(11,256)), using
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), using
- Reed–Solomon code RS(244,256) [i]
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), 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(12877, 65574, S128, 28) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25667, 53688, F256, 2, 28) (dual of [(53688, 2), 107309, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25667, 53688, F256, 3, 28) (dual of [(53688, 3), 160997, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(25667, 53688, F256, 4, 28) (dual of [(53688, 4), 214685, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(25667, 53688, F256, 5, 28) (dual of [(53688, 5), 268373, 29]-NRT-code) | [i] | ||
| 6 | Linear OOA(25667, 53688, F256, 6, 28) (dual of [(53688, 6), 322061, 29]-NRT-code) | [i] | ||
| 7 | Digital (39, 67, 53688)-net over F256 | [i] | ||
| 8 | Linear OOA(25667, 32787, F256, 2, 28) (dual of [(32787, 2), 65507, 29]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25667, 21858, F256, 3, 28) (dual of [(21858, 3), 65507, 29]-NRT-code) | [i] | ||
| 10 | Linear OOA(25667, 16393, F256, 4, 28) (dual of [(16393, 4), 65505, 29]-NRT-code) | [i] | ||
| 11 | Linear OOA(25667, 10929, F256, 6, 28) (dual of [(10929, 6), 65507, 29]-NRT-code) | [i] | ||