Information on Result #731861
Linear OA(545, 390659, F5, 7) (dual of [390659, 390614, 8]-code), using (u, u+v)-construction based on
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- linear OA(541, 390633, F5, 7) (dual of [390633, 390592, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- 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(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(50, 8, F5, 0) (dual of [8, 8, 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(6) ⊂ Ce(5) [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(545, 390659, F5, 2, 7) (dual of [(390659, 2), 781273, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(545, 390659, F5, 3, 7) (dual of [(390659, 3), 1171932, 8]-NRT-code) | [i] | ||
| 3 | Digital (38, 45, 390659)-net over F5 | [i] | ||
| 4 | Linear OOA(545, 195329, F5, 2, 7) (dual of [(195329, 2), 390613, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(545, 130219, F5, 3, 7) (dual of [(130219, 3), 390612, 8]-NRT-code) | [i] | ||