Information on Result #698881
Linear OA(6436, 4113, F64, 16) (dual of [4113, 4077, 17]-code), using construction X applied to Ce(15) ⊂ Ce(9) based on
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), 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(3244, 4113, S32, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6436, 3138, F64, 2, 16) (dual of [(3138, 2), 6240, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6436, 3138, F64, 3, 16) (dual of [(3138, 3), 9378, 17]-NRT-code) | [i] | ||
| 4 | Digital (20, 36, 3138)-net over F64 | [i] | ||
| 5 | Linear OOA(6436, 2056, F64, 2, 16) (dual of [(2056, 2), 4076, 17]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6436, 1371, F64, 3, 16) (dual of [(1371, 3), 4077, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(6436, 514, F64, 16, 16) (dual of [(514, 16), 8188, 17]-NRT-code) | [i] | OA Folding and Stacking | |