Information on Result #2676560
Linear OOA(3115, 1594328, F3, 3, 13) (dual of [(1594328, 3), 4782869, 14]-NRT-code), using 31 times duplication based on linear OOA(3114, 1594328, F3, 3, 13) (dual of [(1594328, 3), 4782870, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3114, 4782984, F3, 13) (dual of [4782984, 4782870, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [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(3115, 1594328, F3, 4, 13) (dual of [(1594328, 4), 6377197, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3115, 1594328, F3, 5, 13) (dual of [(1594328, 5), 7971525, 14]-NRT-code) | [i] | ||
| 3 | Digital (102, 115, 1594328)-net over F3 | [i] | ||