Information on Result #698830
Linear OA(6426, 4107, F64, 12) (dual of [4107, 4081, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) 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(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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(3232, 4107, S32, 12) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6426, 2351, F64, 2, 12) (dual of [(2351, 2), 4676, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6426, 2351, F64, 3, 12) (dual of [(2351, 3), 7027, 13]-NRT-code) | [i] | ||
| 4 | Digital (14, 26, 2351)-net over F64 | [i] | ||
| 5 | Linear OOA(6426, 2053, F64, 2, 12) (dual of [(2053, 2), 4080, 13]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6426, 1369, F64, 3, 12) (dual of [(1369, 3), 4081, 13]-NRT-code) | [i] | ||