Information on Result #2228374
Linear OA(349, 531454, F3, 6) (dual of [531454, 531405, 7]-code), using 1 times truncation 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
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(349, 531454, F3, 2, 6) (dual of [(531454, 2), 1062859, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(349, 531454, F3, 3, 6) (dual of [(531454, 3), 1594313, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(349, 531454, F3, 4, 6) (dual of [(531454, 4), 2125767, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(349, 531454, F3, 5, 6) (dual of [(531454, 5), 2657221, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(349, 265727, F3, 2, 6) (dual of [(265727, 2), 531405, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(349, 177151, F3, 3, 6) (dual of [(177151, 3), 531404, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(349, 177151, F3, 4, 6) (dual of [(177151, 4), 708555, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 8 | Linear OOA(349, 177151, F3, 5, 6) (dual of [(177151, 5), 885706, 7]-NRT-code) | [i] | ||