Information on Result #2255083
Linear OA(1678, 1048593, F16, 16) (dual of [1048593, 1048515, 17]-code), using 1 times truncation based on linear OA(1679, 1048594, F16, 17) (dual of [1048594, 1048515, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), 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(1678, 1048593, F16, 2, 16) (dual of [(1048593, 2), 2097108, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (62, 78, 1048593)-net over F16 | [i] | ||
| 3 | Linear OA(1679, 1048595, F16, 16) (dual of [1048595, 1048516, 17]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(1678, 524296, F16, 2, 16) (dual of [(524296, 2), 1048514, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1678, 131074, F16, 16, 16) (dual of [(131074, 16), 2097106, 17]-NRT-code) | [i] | OA Folding and Stacking | |