Information on Result #738450
Linear OA(556, 78162, F5, 9) (dual of [78162, 78106, 10]-code), using (u, u+v)-construction based on
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- linear OA(550, 78132, F5, 9) (dual of [78132, 78082, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [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(556, 78162, F5, 2, 9) (dual of [(78162, 2), 156268, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(556, 78162, F5, 3, 9) (dual of [(78162, 3), 234430, 10]-NRT-code) | [i] | ||
| 3 | Digital (47, 56, 78162)-net over F5 | [i] | ||
| 4 | Linear OOA(556, 39081, F5, 2, 9) (dual of [(39081, 2), 78106, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(556, 26054, F5, 3, 9) (dual of [(26054, 3), 78106, 10]-NRT-code) | [i] | ||