Information on Result #696652
Linear OA(32108, 1048611, F32, 26) (dual of [1048611, 1048503, 27]-code), using construction X applied to Ce(25) ⊂ Ce(18) based on
- linear OA(32101, 1048576, F32, 26) (dual of [1048576, 1048475, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(327, 35, F32, 6) (dual of [35, 28, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(327, 43, F32, 6) (dual of [43, 36, 7]-code), using
- algebraic-geometric code AG(F,36P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- discarding factors / shortening the dual code based on linear OA(327, 43, F32, 6) (dual of [43, 36, 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(32108, 1048611, F32, 2, 26) (dual of [(1048611, 2), 2097114, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (82, 108, 1048611)-net over F32 | [i] | ||
| 3 | Linear OOA(32108, 524305, F32, 2, 26) (dual of [(524305, 2), 1048502, 27]-NRT-code) | [i] | OOA Folding | |