Information on Result #2677376
Linear OOA(3173, 177157, F3, 3, 21) (dual of [(177157, 3), 531298, 22]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3170, 177156, F3, 3, 21) (dual of [(177156, 3), 531298, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3170, 531468, F3, 21) (dual of [531468, 531298, 22]-code), using
- construction X4 applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3169, 531442, F3, 21) (dual of [531442, 531273, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,10]) ⊂ 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(3174, 177157, F3, 3, 21) (dual of [(177157, 3), 531297, 22]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3173, 177157, F3, 4, 21) (dual of [(177157, 4), 708455, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3173, 177157, F3, 5, 21) (dual of [(177157, 5), 885612, 22]-NRT-code) | [i] | ||
| 4 | Digital (152, 173, 177157)-net over F3 | [i] | ||