Information on Result #734977
Linear OA(6451, 4180, F64, 20) (dual of [4180, 4129, 21]-code), using (u, u+v)-construction based on
- linear OA(6412, 82, F64, 10) (dual of [82, 70, 11]-code), using
- construction X applied to AG(F,68P) ⊂ AG(F,70P) [i] based on
- linear OA(6411, 79, F64, 10) (dual of [79, 68, 11]-code), using algebraic-geometric code AG(F,68P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- linear OA(649, 79, F64, 8) (dual of [79, 70, 9]-code), using algebraic-geometric code AG(F,70P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80 (see above)
- linear OA(641, 3, F64, 1) (dual of [3, 2, 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
- construction X applied to AG(F,68P) ⊂ AG(F,70P) [i] based on
- linear OA(6439, 4098, F64, 20) (dual of [4098, 4059, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [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(6451, 2090, F64, 2, 20) (dual of [(2090, 2), 4129, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(6451, 1393, F64, 3, 20) (dual of [(1393, 3), 4128, 21]-NRT-code) | [i] | ||