Information on Result #691854
Linear OA(16129, 65568, F16, 33) (dual of [65568, 65439, 34]-code), using construction X applied to Ce(32) ⊂ Ce(25) based on
- linear OA(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(168, 32, F16, 6) (dual of [32, 24, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(168, 33, F16, 6) (dual of [33, 25, 7]-code), using
- extended algebraic-geometric code AGe(F,26P) [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- discarding factors / shortening the dual code based on linear OA(168, 33, F16, 6) (dual of [33, 25, 7]-code), 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(16129, 65568, F16, 2, 33) (dual of [(65568, 2), 131007, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (96, 129, 65568)-net over F16 | [i] | ||
| 3 | Linear OOA(16129, 32784, F16, 2, 33) (dual of [(32784, 2), 65439, 34]-NRT-code) | [i] | OOA Folding | |