Information on Result #2485401
Linear OOA(376, 265728, F3, 2, 10) (dual of [(265728, 2), 531380, 11]-NRT-code), using 31 times duplication based on linear OOA(375, 265728, F3, 2, 10) (dual of [(265728, 2), 531381, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(375, 531456, F3, 10) (dual of [531456, 531381, 11]-code), using
- 1 times code embedding in larger space [i] based on linear OA(374, 531455, F3, 10) (dual of [531455, 531381, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(9) ⊂ Ce(7) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(374, 531455, F3, 10) (dual of [531455, 531381, 11]-code), 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(376, 186951, F3, 3, 10) (dual of [(186951, 3), 560777, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(376, 186951, F3, 4, 10) (dual of [(186951, 4), 747728, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(376, 186951, F3, 5, 10) (dual of [(186951, 5), 934679, 11]-NRT-code) | [i] | ||
| 4 | Digital (66, 76, 186951)-net over F3 | [i] | ||