Information on Result #2281461
Linear OA(8164, 2097168, F8, 27) (dual of [2097168, 2097004, 28]-code), using 1 times code embedding in larger space based on linear OA(8163, 2097167, F8, 27) (dual of [2097167, 2097004, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(8164, 1123747, F8, 2, 27) (dual of [(1123747, 2), 2247330, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8164, 1123747, F8, 3, 27) (dual of [(1123747, 3), 3371077, 28]-NRT-code) | [i] | ||
| 3 | Digital (137, 164, 1123747)-net over F8 | [i] | ||
| 4 | Linear OOA(8164, 1048584, F8, 2, 27) (dual of [(1048584, 2), 2097004, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8164, 699056, F8, 3, 27) (dual of [(699056, 3), 2097004, 28]-NRT-code) | [i] | ||