Information on Result #700282
Linear OA(25654, 65566, F256, 23) (dual of [65566, 65512, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,6]) based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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(12862, 65566, S128, 23) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25654, 40718, F256, 2, 23) (dual of [(40718, 2), 81382, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25654, 40718, F256, 3, 23) (dual of [(40718, 3), 122100, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(25654, 40718, F256, 4, 23) (dual of [(40718, 4), 162818, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(25654, 40718, F256, 5, 23) (dual of [(40718, 5), 203536, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(25654, 40718, F256, 6, 23) (dual of [(40718, 6), 244254, 24]-NRT-code) | [i] | ||
| 7 | Digital (31, 54, 40718)-net over F256 | [i] | ||
| 8 | Linear OOA(25654, 32783, F256, 2, 23) (dual of [(32783, 2), 65512, 24]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25654, 21855, F256, 3, 23) (dual of [(21855, 3), 65511, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(25654, 16391, F256, 4, 23) (dual of [(16391, 4), 65510, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(25654, 13113, F256, 5, 23) (dual of [(13113, 5), 65511, 24]-NRT-code) | [i] | ||