Information on Result #698498
Linear OA(6421, 262155, F64, 7) (dual of [262155, 262134, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), 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 | Linear OOA(6421, 262155, F64, 2, 7) (dual of [(262155, 2), 524289, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6421, 262155, F64, 3, 7) (dual of [(262155, 3), 786444, 8]-NRT-code) | [i] | ||
| 3 | Digital (14, 21, 262155)-net over F64 | [i] | ||
| 4 | Linear OOA(6421, 131077, F64, 2, 7) (dual of [(131077, 2), 262133, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6421, 87385, F64, 3, 7) (dual of [(87385, 3), 262134, 8]-NRT-code) | [i] | ||