Information on Result #1303038
Linear OA(8165, 524296, F8, 28) (dual of [524296, 524131, 29]-code), using construction X with Varšamov bound based on
- linear OA(8164, 524294, F8, 28) (dual of [524294, 524130, 29]-code), using
- trace code [i] based on linear OA(6482, 262147, F64, 28) (dual of [262147, 262065, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(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(27) ⊂ Ce(26) [i] based on
- trace code [i] based on linear OA(6482, 262147, F64, 28) (dual of [262147, 262065, 29]-code), using
- linear OA(8164, 524295, F8, 27) (dual of [524295, 524131, 28]-code), using Gilbert–Varšamov bound and bm = 8164 > Vbs−1(k−1) = 1 190175 360518 227145 312742 993634 217906 384889 507672 142228 786028 976818 083995 727836 965157 319194 696140 035952 968738 635573 077380 809873 830043 009799 290880 [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(8165, 524296, F8, 2, 28) (dual of [(524296, 2), 1048427, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8165, 524296, F8, 3, 28) (dual of [(524296, 3), 1572723, 29]-NRT-code) | [i] | ||
| 3 | Digital (137, 165, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(8165, 262148, F8, 2, 28) (dual of [(262148, 2), 524131, 29]-NRT-code) | [i] | OOA Folding | |