Information on Result #700466
Linear OA(25652, 65565, F256, 22) (dual of [65565, 65513, 23]-code), using construction X applied to Ce(21) ⊂ Ce(11) based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2569, 29, F256, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,256)), using
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- Reed–Solomon code RS(247,256) [i]
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), 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(12860, 65565, S128, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25652, 45050, F256, 2, 22) (dual of [(45050, 2), 90048, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25652, 45050, F256, 3, 22) (dual of [(45050, 3), 135098, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(25652, 45050, F256, 4, 22) (dual of [(45050, 4), 180148, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(25652, 45050, F256, 5, 22) (dual of [(45050, 5), 225198, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(25652, 45050, F256, 6, 22) (dual of [(45050, 6), 270248, 23]-NRT-code) | [i] | ||
| 7 | Digital (30, 52, 45050)-net over F256 | [i] | ||
| 8 | Linear OOA(25652, 32782, F256, 2, 22) (dual of [(32782, 2), 65512, 23]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25652, 21855, F256, 3, 22) (dual of [(21855, 3), 65513, 23]-NRT-code) | [i] | ||
| 10 | Linear OOA(25652, 16391, F256, 4, 22) (dual of [(16391, 4), 65512, 23]-NRT-code) | [i] | ||
| 11 | Linear OOA(25652, 13113, F256, 5, 22) (dual of [(13113, 5), 65513, 23]-NRT-code) | [i] | ||