Information on Result #812671
Linear OOA(362, 265727, F3, 2, 8) (dual of [(265727, 2), 531392, 9]-NRT-code), using OOA 2-folding based on linear OA(362, 531454, F3, 8) (dual of [531454, 531392, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(362, 531455, F3, 8) (dual of [531455, 531393, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(361, 531441, F3, 8) (dual of [531441, 531380, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(7) ⊂ Ce(6) [i] based on
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(362, 265727, F3, 3, 8) (dual of [(265727, 3), 797119, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(362, 265727, F3, 4, 8) (dual of [(265727, 4), 1062846, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(362, 265727, F3, 5, 8) (dual of [(265727, 5), 1328573, 9]-NRT-code) | [i] | ||
| 4 | Digital (54, 62, 265727)-net over F3 | [i] | ||