Information on Result #2628293
Linear OOA(3236, 1594345, F3, 3, 24) (dual of [(1594345, 3), 4782799, 25]-NRT-code), using strength reduction based on linear OOA(3236, 1594345, F3, 3, 25) (dual of [(1594345, 3), 4782799, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3236, 4783035, F3, 25) (dual of [4783035, 4782799, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-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(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 4783037, F3, 25) (dual of [4783037, 4782801, 26]-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(3236, 1502219, F3, 4, 24) (dual of [(1502219, 4), 6008640, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3236, 1502219, F3, 5, 24) (dual of [(1502219, 5), 7510859, 25]-NRT-code) | [i] | ||
| 3 | Digital (212, 236, 1502219)-net over F3 | [i] | ||