Information on Result #731129
Linear OA(864, 8202, F8, 16) (dual of [8202, 8138, 17]-code), using trace code based on linear OA(6432, 4101, F64, 16) (dual of [4101, 4069, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] 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(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(865, 8203, F8, 16) (dual of [8203, 8138, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(864, 8202, F8, 2, 16) (dual of [(8202, 2), 16340, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(864, 8202, F8, 3, 16) (dual of [(8202, 3), 24542, 17]-NRT-code) | [i] | ||
| 4 | Digital (48, 64, 8202)-net over F8 | [i] | ||
| 5 | Linear OA(865, 8204, F8, 16) (dual of [8204, 8139, 17]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(864, 4101, F8, 2, 16) (dual of [(4101, 2), 8138, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(864, 2734, F8, 3, 16) (dual of [(2734, 3), 8138, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(864, 1025, F8, 16, 16) (dual of [(1025, 16), 16336, 17]-NRT-code) | [i] | OA Folding and Stacking | |