Information on Result #953401
Linear OOA(3234, 1594345, F3, 3, 24) (dual of [(1594345, 3), 4782801, 25]-NRT-code), using OOA 3-folding based on linear OA(3234, 4783035, F3, 24) (dual of [4783035, 4782801, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(39, 65, F3, 4) (dual of [65, 56, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-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(3235, 1594345, F3, 3, 24) (dual of [(1594345, 3), 4782800, 25]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3234, 1345924, F3, 4, 24) (dual of [(1345924, 4), 5383462, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3234, 1345924, F3, 5, 24) (dual of [(1345924, 5), 6729386, 25]-NRT-code) | [i] | ||
| 4 | Digital (210, 234, 1345924)-net over F3 | [i] | ||