Information on Result #700411
Linear OA(25623, 65550, F256, 10) (dual of [65550, 65527, 11]-code), using construction X applied to Ce(9) ⊂ Ce(4) based on
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2569, 65536, F256, 5) (dual of [65536, 65527, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), 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(12827, 65550, S128, 10) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25623, 61914, F256, 2, 10) (dual of [(61914, 2), 123805, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25623, 61914, F256, 3, 10) (dual of [(61914, 3), 185719, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(25623, 61914, F256, 4, 10) (dual of [(61914, 4), 247633, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(25623, 61914, F256, 5, 10) (dual of [(61914, 5), 309547, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(25623, 61914, F256, 6, 10) (dual of [(61914, 6), 371461, 11]-NRT-code) | [i] | ||
| 7 | Digital (13, 23, 61914)-net over F256 | [i] | ||
| 8 | Linear OOA(25623, 32775, F256, 2, 10) (dual of [(32775, 2), 65527, 11]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25623, 21850, F256, 3, 10) (dual of [(21850, 3), 65527, 11]-NRT-code) | [i] | ||
| 10 | Linear OOA(25623, 16387, F256, 4, 10) (dual of [(16387, 4), 65525, 11]-NRT-code) | [i] | ||
| 11 | Linear OOA(25623, 13110, F256, 5, 10) (dual of [(13110, 5), 65527, 11]-NRT-code) | [i] | ||
| 12 | Linear OOA(25623, 13110, F256, 6, 10) (dual of [(13110, 6), 78637, 11]-NRT-code) | [i] | OA Folding and Stacking | |
| 13 | Linear OOA(25623, 13110, F256, 10, 10) (dual of [(13110, 10), 131077, 11]-NRT-code) | [i] | ||