Information on Result #731859
Linear OA(535, 15657, F5, 7) (dual of [15657, 15622, 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(531, 15631, F5, 7) (dual of [15631, 15600, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(531, 15625, F5, 7) (dual of [15625, 15594, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 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(535, 15657, F5, 2, 7) (dual of [(15657, 2), 31279, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(535, 15657, F5, 3, 7) (dual of [(15657, 3), 46936, 8]-NRT-code) | [i] | ||
| 3 | Digital (28, 35, 15657)-net over F5 | [i] | ||
| 4 | Linear OOA(535, 7828, F5, 2, 7) (dual of [(7828, 2), 15621, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(535, 5219, F5, 3, 7) (dual of [(5219, 3), 15622, 8]-NRT-code) | [i] | ||