Information on Result #612094
Linear OA(3156, 2204, F3, 31) (dual of [2204, 2048, 32]-code), using construction X applied to C([0,15]) ⊂ C([1,15]) based on
- linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3140, 2188, F3, 15) (dual of [2188, 2048, 16]-code), using the narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
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(3156, 2044, F3, 2, 31) (dual of [(2044, 2), 3932, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3156, 2044, F3, 3, 31) (dual of [(2044, 3), 5976, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3156, 2044, F3, 4, 31) (dual of [(2044, 4), 8020, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3156, 2044, F3, 5, 31) (dual of [(2044, 5), 10064, 32]-NRT-code) | [i] | ||
| 5 | Digital (125, 156, 2044)-net over F3 | [i] | ||