Information on Result #844847
Linear OOA(8156, 1048580, F8, 2, 26) (dual of [(1048580, 2), 2097004, 27]-NRT-code), using OOA 2-folding based on linear OA(8156, 2097160, F8, 26) (dual of [2097160, 2097004, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8155, 2097159, F8, 26) (dual of [2097159, 2097004, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(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(25) ⊂ Ce(24) [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(8156, 1048580, F8, 3, 26) (dual of [(1048580, 3), 3145584, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (130, 156, 1048580)-net over F8 | [i] | ||