Information on Result #812652
Linear OOA(337, 1098, F3, 2, 8) (dual of [(1098, 2), 2159, 9]-NRT-code), using OOA 2-folding based on linear OA(337, 2196, F3, 8) (dual of [2196, 2159, 9]-code), using
- construction X4 applied to C([0,7]) ⊂ C([1,6]) [i] based on
- linear OA(336, 2186, F3, 8) (dual of [2186, 2150, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(328, 2186, F3, 6) (dual of [2186, 2158, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(39, 10, F3, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
- dual of repetition code with length 10 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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(338, 1098, F3, 2, 8) (dual of [(1098, 2), 2158, 9]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3188, 4195399, F3, 2, 16) (dual of [(4195399, 2), 8390610, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 3 | Linear OOA(3203, 4195399, F3, 2, 17) (dual of [(4195399, 2), 8390595, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(337, 1098, F3, 3, 8) (dual of [(1098, 3), 3257, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(337, 1098, F3, 4, 8) (dual of [(1098, 4), 4355, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(337, 1098, F3, 5, 8) (dual of [(1098, 5), 5453, 9]-NRT-code) | [i] | ||
| 7 | Digital (29, 37, 1098)-net over F3 | [i] | ||