Information on Result #698563
Linear OA(6453, 262175, F64, 16) (dual of [262175, 262122, 17]-code), using construction X applied to Ce(15) ⊂ Ce(7) based on
- linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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 | Linear OOA(6453, 262175, F64, 2, 16) (dual of [(262175, 2), 524297, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6453, 262175, F64, 3, 16) (dual of [(262175, 3), 786472, 17]-NRT-code) | [i] | ||
| 3 | Digital (37, 53, 262175)-net over F64 | [i] | ||
| 4 | Linear OOA(6453, 131087, F64, 2, 16) (dual of [(131087, 2), 262121, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(6453, 87391, F64, 3, 16) (dual of [(87391, 3), 262120, 17]-NRT-code) | [i] | ||