Information on Result #2277335
Linear OA(5133, 1953158, F5, 18) (dual of [1953158, 1953025, 19]-code), using 1 times code embedding in larger space based on linear OA(5132, 1953157, F5, 18) (dual of [1953157, 1953025, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(5127, 1953125, F5, 18) (dual of [1953125, 1952998, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), 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 OOA(5133, 993062, F5, 2, 18) (dual of [(993062, 2), 1985991, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5133, 993062, F5, 3, 18) (dual of [(993062, 3), 2979053, 19]-NRT-code) | [i] | ||
| 3 | Digital (115, 133, 993062)-net over F5 | [i] | ||
| 4 | Linear OOA(5133, 976579, F5, 2, 18) (dual of [(976579, 2), 1953025, 19]-NRT-code) | [i] | OOA Folding | |