Information on Result #953056
Linear OOA(3184, 531450, F3, 3, 21) (dual of [(531450, 3), 1594166, 22]-NRT-code), using OOA 3-folding based on linear OA(3184, 1594350, F3, 21) (dual of [1594350, 1594166, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3184, 1594351, F3, 21) (dual of [1594351, 1594167, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3183, 1594324, F3, 21) (dual of [1594324, 1594141, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(31, 27, F3, 1) (dual of [27, 26, 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 C([0,10]) ⊂ C([0,9]) [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(3184, 431357, F3, 4, 21) (dual of [(431357, 4), 1725244, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3184, 431357, F3, 5, 21) (dual of [(431357, 5), 2156601, 22]-NRT-code) | [i] | ||
| 3 | Digital (163, 184, 431357)-net over F3 | [i] | ||