Information on Result #2486052
Linear OOA(3126, 265736, F3, 2, 15) (dual of [(265736, 2), 531346, 16]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(3122, 265734, F3, 2, 15) (dual of [(265734, 2), 531346, 16]-NRT-code), using
- OOA 2-folding [i] 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
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [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(3126, 225197, F3, 3, 15) (dual of [(225197, 3), 675465, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3126, 225197, F3, 4, 15) (dual of [(225197, 4), 900662, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(3126, 225197, F3, 5, 15) (dual of [(225197, 5), 1125859, 16]-NRT-code) | [i] | ||
| 4 | Digital (111, 126, 225197)-net over F3 | [i] | ||