Information on Result #731862
Linear OA(550, 1953160, F5, 7) (dual of [1953160, 1953110, 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(546, 1953134, F5, 7) (dual of [1953134, 1953088, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(546, 1953125, F5, 7) (dual of [1953125, 1953079, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(50, 9, F5, 0) (dual of [9, 9, 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(550, 1953160, F5, 2, 7) (dual of [(1953160, 2), 3906270, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(550, 1953160, F5, 3, 7) (dual of [(1953160, 3), 5859430, 8]-NRT-code) | [i] | ||
| 3 | Digital (43, 50, 1953160)-net over F5 | [i] | ||
| 4 | Linear OOA(550, 976580, F5, 2, 7) (dual of [(976580, 2), 1953110, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(550, 651053, F5, 3, 7) (dual of [(651053, 3), 1953109, 8]-NRT-code) | [i] | ||