Information on Result #682288
Linear OA(558, 390643, F5, 9) (dual of [390643, 390585, 10]-code), using construction X4 applied to Ce(8) ⊂ Ce(6) based on
- linear OA(557, 390625, F5, 9) (dual of [390625, 390568, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(541, 390625, F5, 7) (dual of [390625, 390584, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(559, 390644, F5, 9) (dual of [390644, 390585, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(558, 390643, F5, 2, 9) (dual of [(390643, 2), 781228, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(558, 390643, F5, 3, 9) (dual of [(390643, 3), 1171871, 10]-NRT-code) | [i] | ||
| 4 | Digital (49, 58, 390643)-net over F5 | [i] | ||
| 5 | Linear OA(559, 390645, F5, 9) (dual of [390645, 390586, 10]-code) | [i] | Construction X with Varšamov Bound | |