Information on Result #682286
Linear OA(566, 390643, F5, 10) (dual of [390643, 390577, 11]-code), using construction X4 applied to Ce(10) ⊂ Ce(7) based on
- linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(549, 390625, F5, 8) (dual of [390625, 390576, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(517, 18, F5, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,5)), using
- dual of repetition code with length 18 [i]
- linear OA(51, 18, F5, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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 OA(567, 390644, F5, 10) (dual of [390644, 390577, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(566, 390643, F5, 2, 10) (dual of [(390643, 2), 781220, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(566, 390643, F5, 3, 10) (dual of [(390643, 3), 1171863, 11]-NRT-code) | [i] | ||
| 4 | Digital (56, 66, 390643)-net over F5 | [i] | ||
| 5 | Linear OA(567, 390645, F5, 10) (dual of [390645, 390578, 11]-code) | [i] | Construction X with Varšamov Bound | |