Information on Result #952471
Linear OOA(3122, 177156, F3, 3, 15) (dual of [(177156, 3), 531346, 16]-NRT-code), using OOA 3-folding based on linear OA(3122, 531468, F3, 15) (dual of [531468, 531346, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3121, 531442, F3, 15) (dual of [531442, 531321, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(397, 531442, F3, 13) (dual of [531442, 531345, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
- dual of repetition code with length 26 [i]
- linear OA(31, 26, F3, 1) (dual of [26, 25, 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
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(3125, 177157, F3, 3, 15) (dual of [(177157, 3), 531346, 16]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3123, 177156, F3, 3, 15) (dual of [(177156, 3), 531345, 16]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3124, 177156, F3, 3, 15) (dual of [(177156, 3), 531344, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(3122, 177156, F3, 4, 15) (dual of [(177156, 4), 708502, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3122, 177156, F3, 5, 15) (dual of [(177156, 5), 885658, 16]-NRT-code) | [i] | ||
| 6 | Digital (107, 122, 177156)-net over F3 | [i] | ||