Information on Result #845068
Linear OOA(8169, 1048579, F8, 2, 28) (dual of [(1048579, 2), 2096989, 29]-NRT-code), using OOA 2-folding based on linear OA(8169, 2097158, F8, 28) (dual of [2097158, 2096989, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8169, 2097159, F8, 28) (dual of [2097159, 2096990, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(8169, 2097152, F8, 28) (dual of [2097152, 2096983, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(80, 7, F8, 0) (dual of [7, 7, 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
- construction X applied to Ce(27) ⊂ Ce(26) [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(8169, 1048579, F8, 3, 28) (dual of [(1048579, 3), 3145568, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (141, 169, 1048579)-net over F8 | [i] | ||