Information on Result #1361864
Linear OOA(352, 265729, F3, 2, 7) (dual of [(265729, 2), 531406, 8]-NRT-code), using OOA 2-folding based on linear OA(352, 531458, F3, 7) (dual of [531458, 531406, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(350, 531455, F3, 7) (dual of [531455, 531405, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(349, 531441, F3, 7) (dual of [531441, 531392, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(337, 531441, F3, 5) (dual of [531441, 531404, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- dual of repetition code with length 14 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 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 Ce(6) ⊂ Ce(4) [i] based on
- linear OA(350, 531456, F3, 5) (dual of [531456, 531406, 6]-code), using Gilbert–Varšamov bound and bm = 350 > Vbs−1(k−1) = 53182 832189 907376 025611 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 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 (see above)
- linear OA(350, 531455, F3, 7) (dual of [531455, 531405, 8]-code), using
Mode: 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(352, 265729, F3, 3, 7) (dual of [(265729, 3), 797135, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(352, 265729, F3, 4, 7) (dual of [(265729, 4), 1062864, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(352, 265729, F3, 5, 7) (dual of [(265729, 5), 1328593, 8]-NRT-code) | [i] | ||
| 4 | Digital (45, 52, 265729)-net over F3 | [i] | ||