Information on Result #2677005
Linear OOA(3153, 531457, F3, 3, 17) (dual of [(531457, 3), 1594218, 18]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3150, 531456, F3, 3, 17) (dual of [(531456, 3), 1594218, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3150, 1594368, F3, 17) (dual of [1594368, 1594218, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(16) ⊂ Ce(12) [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(3154, 531457, F3, 3, 17) (dual of [(531457, 3), 1594217, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3153, 531457, F3, 4, 17) (dual of [(531457, 4), 2125675, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3153, 531457, F3, 5, 17) (dual of [(531457, 5), 2657132, 18]-NRT-code) | [i] | ||
| 4 | Digital (136, 153, 531457)-net over F3 | [i] | ||