Information on Result #1303003
Linear OA(8159, 524296, F8, 27) (dual of [524296, 524137, 28]-code), using construction X with Varšamov bound based on
- linear OA(8158, 524294, F8, 27) (dual of [524294, 524136, 28]-code), using
- trace code [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 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(26) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- linear OA(8158, 524295, F8, 26) (dual of [524295, 524137, 27]-code), using Gilbert–Varšamov bound and bm = 8158 > Vbs−1(k−1) = 8 432026 563513 827178 345508 861969 177582 961734 988829 629992 203844 978636 232948 221105 267559 713703 672892 459483 625264 206202 464720 137288 951038 541824 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(8159, 524296, F8, 2, 27) (dual of [(524296, 2), 1048433, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8159, 524296, F8, 3, 27) (dual of [(524296, 3), 1572729, 28]-NRT-code) | [i] | ||
| 3 | Digital (132, 159, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(8159, 262148, F8, 2, 27) (dual of [(262148, 2), 524137, 28]-NRT-code) | [i] | OOA Folding | |