Information on Result #700286
Linear OA(25660, 65572, F256, 25) (dual of [65572, 65512, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,6]) based on
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(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(12869, 65572, S128, 25) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25660, 55654, F256, 2, 25) (dual of [(55654, 2), 111248, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25660, 55654, F256, 3, 25) (dual of [(55654, 3), 166902, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(25660, 55654, F256, 4, 25) (dual of [(55654, 4), 222556, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(25660, 55654, F256, 5, 25) (dual of [(55654, 5), 278210, 26]-NRT-code) | [i] | ||
| 6 | Linear OOA(25660, 55654, F256, 6, 25) (dual of [(55654, 6), 333864, 26]-NRT-code) | [i] | ||
| 7 | Digital (35, 60, 55654)-net over F256 | [i] | ||
| 8 | Linear OOA(25660, 32786, F256, 2, 25) (dual of [(32786, 2), 65512, 26]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25660, 21857, F256, 3, 25) (dual of [(21857, 3), 65511, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(25660, 16393, F256, 4, 25) (dual of [(16393, 4), 65512, 26]-NRT-code) | [i] | ||
| 11 | Linear OOA(25660, 13114, F256, 5, 25) (dual of [(13114, 5), 65510, 26]-NRT-code) | [i] | ||
| 12 | Linear OOA(25660, 5464, F256, 25, 25) (dual of [(5464, 25), 136540, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |