Information on Result #674571
Linear OA(350, 531467, F3, 6) (dual of [531467, 531417, 7]-code), using construction X4 applied to Ce(6) ⊂ Ce(3) 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(325, 531441, F3, 4) (dual of [531441, 531416, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
- dual of repetition code with length 26 [i]
- linear OA(31, 26, F3, 1) (dual of [26, 25, 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 OA(351, 531468, F3, 6) (dual of [531468, 531417, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(350, 531467, F3, 2, 6) (dual of [(531467, 2), 1062884, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(350, 531467, F3, 3, 6) (dual of [(531467, 3), 1594351, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(350, 531467, F3, 4, 6) (dual of [(531467, 4), 2125818, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(350, 531467, F3, 5, 6) (dual of [(531467, 5), 2657285, 7]-NRT-code) | [i] | ||
| 6 | Linear OA(351, 531469, F3, 6) (dual of [531469, 531418, 7]-code) | [i] | Construction X with Varšamov Bound | |