Information on Result #698865
Linear OA(6427, 4110, F64, 12) (dual of [4110, 4083, 13]-code), using construction X applied to Ce(11) ⊂ Ce(6) based on
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), 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(3233, 4110, S32, 12) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6427, 3566, F64, 2, 12) (dual of [(3566, 2), 7105, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6427, 3566, F64, 3, 12) (dual of [(3566, 3), 10671, 13]-NRT-code) | [i] | ||
| 4 | Digital (15, 27, 3566)-net over F64 | [i] | ||
| 5 | Linear OOA(6427, 2055, F64, 2, 12) (dual of [(2055, 2), 4083, 13]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6427, 1370, F64, 3, 12) (dual of [(1370, 3), 4083, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(6427, 685, F64, 12, 12) (dual of [(685, 12), 8193, 13]-NRT-code) | [i] | OA Folding and Stacking | |