Information on Result #698513
Linear OA(6486, 262163, F64, 28) (dual of [262163, 262077, 29]-code), using construction X applied to Ce(27) ⊂ Ce(22) based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-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(16129, 262163, S16, 28) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(32104, 262163, S32, 28) | [i] | ||
| 3 | Linear OOA(6486, 134503, F64, 2, 28) (dual of [(134503, 2), 268920, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6486, 134503, F64, 3, 28) (dual of [(134503, 3), 403423, 29]-NRT-code) | [i] | ||
| 5 | Digital (58, 86, 134503)-net over F64 | [i] | ||
| 6 | Linear OOA(6486, 131081, F64, 2, 28) (dual of [(131081, 2), 262076, 29]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6486, 87387, F64, 3, 28) (dual of [(87387, 3), 262075, 29]-NRT-code) | [i] | ||