Information on Result #700284
Linear OA(25668, 65572, F256, 29) (dual of [65572, 65504, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,8]) based on
- linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(25611, 35, F256, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,256)), using
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- Reed–Solomon code RS(245,256) [i]
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), 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(12878, 65572, S128, 29) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25668, 40526, F256, 2, 29) (dual of [(40526, 2), 80984, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25668, 40526, F256, 3, 29) (dual of [(40526, 3), 121510, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(25668, 40526, F256, 4, 29) (dual of [(40526, 4), 162036, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(25668, 40526, F256, 5, 29) (dual of [(40526, 5), 202562, 30]-NRT-code) | [i] | ||
| 6 | Linear OOA(25668, 40526, F256, 6, 29) (dual of [(40526, 6), 243088, 30]-NRT-code) | [i] | ||
| 7 | Digital (39, 68, 40526)-net over F256 | [i] | ||
| 8 | Linear OOA(25668, 32786, F256, 2, 29) (dual of [(32786, 2), 65504, 30]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25668, 21857, F256, 3, 29) (dual of [(21857, 3), 65503, 30]-NRT-code) | [i] | ||
| 10 | Linear OOA(25668, 16393, F256, 4, 29) (dual of [(16393, 4), 65504, 30]-NRT-code) | [i] | ||
| 11 | Linear OOA(25668, 13114, F256, 5, 29) (dual of [(13114, 5), 65502, 30]-NRT-code) | [i] | ||