Information on Result #731860
Linear OA(540, 78158, F5, 7) (dual of [78158, 78118, 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(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(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(540, 78158, F5, 2, 7) (dual of [(78158, 2), 156276, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(540, 78158, F5, 3, 7) (dual of [(78158, 3), 234434, 8]-NRT-code) | [i] | ||
| 3 | Digital (33, 40, 78158)-net over F5 | [i] | ||
| 4 | Linear OOA(540, 39079, F5, 2, 7) (dual of [(39079, 2), 78118, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(540, 26052, F5, 3, 7) (dual of [(26052, 3), 78116, 8]-NRT-code) | [i] | ||