Information on Result #735511
Linear OA(12878, 16580, F128, 30) (dual of [16580, 16502, 31]-code), using (u, u+v)-construction based on
- linear OA(12819, 194, F128, 15) (dual of [194, 175, 16]-code), using
- construction X applied to AG(F,175P) ⊂ AG(F,177P) [i] based on
- linear OA(12818, 191, F128, 15) (dual of [191, 173, 16]-code), using algebraic-geometric code AG(F,175P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- linear OA(12816, 191, F128, 13) (dual of [191, 175, 14]-code), using algebraic-geometric code AG(F,177P) [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192 (see above)
- linear OA(1281, 3, F128, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,175P) ⊂ AG(F,177P) [i] based on
- linear OA(12859, 16386, F128, 30) (dual of [16386, 16327, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
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(12878, 8290, F128, 2, 30) (dual of [(8290, 2), 16502, 31]-NRT-code) | [i] | OOA Folding | |