Information on Result #812727
Linear OOA(374, 265734, F3, 2, 9) (dual of [(265734, 2), 531394, 10]-NRT-code), using OOA 2-folding based on linear OA(374, 531468, F3, 9) (dual of [531468, 531394, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(373, 531442, F3, 9) (dual of [531442, 531369, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(349, 531442, F3, 7) (dual of [531442, 531393, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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(376, 265735, F3, 2, 9) (dual of [(265735, 2), 531394, 10]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(375, 265734, F3, 2, 9) (dual of [(265734, 2), 531393, 10]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(374, 265734, F3, 3, 9) (dual of [(265734, 3), 797128, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(374, 265734, F3, 4, 9) (dual of [(265734, 4), 1062862, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(374, 265734, F3, 5, 9) (dual of [(265734, 5), 1328596, 10]-NRT-code) | [i] | ||
| 6 | Digital (65, 74, 265734)-net over F3 | [i] | ||