Information on Result #2255114
Linear OA(16125, 65556, F16, 32) (dual of [65556, 65431, 33]-code), using 1 times truncation based on linear OA(16126, 65557, F16, 33) (dual of [65557, 65431, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] 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(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(165, 21, F16, 4) (dual of [21, 16, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-code), using
- extended algebraic-geometric code AGe(F,19P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-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 | OA(8167, 65556, S8, 32) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(16125, 65556, F16, 2, 32) (dual of [(65556, 2), 130987, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (93, 125, 65556)-net over F16 | [i] | ||
| 4 | Linear OOA(16125, 32778, F16, 2, 32) (dual of [(32778, 2), 65431, 33]-NRT-code) | [i] | OOA Folding | |