Information on Result #698557
Linear OA(6489, 262175, F64, 28) (dual of [262175, 262086, 29]-code), using construction X applied to Ce(27) ⊂ Ce(19) 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(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(647, 31, F64, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), 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(32107, 262175, S32, 28) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6489, 217346, F64, 2, 28) (dual of [(217346, 2), 434603, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6489, 217346, F64, 3, 28) (dual of [(217346, 3), 651949, 29]-NRT-code) | [i] | ||
| 4 | Digital (61, 89, 217346)-net over F64 | [i] | ||
| 5 | Linear OOA(6489, 131087, F64, 2, 28) (dual of [(131087, 2), 262085, 29]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6489, 87391, F64, 3, 28) (dual of [(87391, 3), 262084, 29]-NRT-code) | [i] | ||