Information on Result #952397
Linear OOA(3122, 531451, F3, 3, 14) (dual of [(531451, 3), 1594231, 15]-NRT-code), using OOA 3-folding based on linear OA(3122, 1594353, F3, 14) (dual of [1594353, 1594231, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 30, F3, 2) (dual of [30, 26, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), 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(3123, 531451, F3, 3, 14) (dual of [(531451, 3), 1594230, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3122, 531451, F3, 4, 14) (dual of [(531451, 4), 2125682, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3122, 531451, F3, 5, 14) (dual of [(531451, 5), 2657133, 15]-NRT-code) | [i] | ||
| 4 | Digital (108, 122, 531451)-net over F3 | [i] | ||