Information on Result #700422
Linear OA(25628, 65553, F256, 12) (dual of [65553, 65525, 13]-code), using construction X applied to Ce(11) ⊂ Ce(5) based on
- 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(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), 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(12832, 65553, S128, 12) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25628, 56449, F256, 2, 12) (dual of [(56449, 2), 112870, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25628, 56449, F256, 3, 12) (dual of [(56449, 3), 169319, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(25628, 56449, F256, 4, 12) (dual of [(56449, 4), 225768, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(25628, 56449, F256, 5, 12) (dual of [(56449, 5), 282217, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(25628, 56449, F256, 6, 12) (dual of [(56449, 6), 338666, 13]-NRT-code) | [i] | ||
| 7 | Digital (16, 28, 56449)-net over F256 | [i] | ||
| 8 | Linear OOA(25628, 32776, F256, 2, 12) (dual of [(32776, 2), 65524, 13]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25628, 21851, F256, 3, 12) (dual of [(21851, 3), 65525, 13]-NRT-code) | [i] | ||
| 10 | Linear OOA(25628, 16388, F256, 4, 12) (dual of [(16388, 4), 65524, 13]-NRT-code) | [i] | ||