Information on Result #2264875
Linear OA(373, 2205, F3, 15) (dual of [2205, 2132, 16]-code), using 1 times code embedding in larger space based on linear OA(372, 2204, F3, 15) (dual of [2204, 2132, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(371, 2188, F3, 15) (dual of [2188, 2117, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(357, 2188, F3, 13) (dual of [2188, 2131, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 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(373, 1232, F3, 2, 15) (dual of [(1232, 2), 2391, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(373, 1232, F3, 3, 15) (dual of [(1232, 3), 3623, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(373, 1232, F3, 4, 15) (dual of [(1232, 4), 4855, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(373, 1232, F3, 5, 15) (dual of [(1232, 5), 6087, 16]-NRT-code) | [i] | ||
| 5 | Digital (58, 73, 1232)-net over F3 | [i] | ||
| 6 | Linear OOA(373, 735, F3, 3, 15) (dual of [(735, 3), 2132, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(373, 441, F3, 5, 15) (dual of [(441, 5), 2132, 16]-NRT-code) | [i] | ||