Information on Result #676697
Linear OA(373, 753, F3, 17) (dual of [753, 680, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
- linear OA(367, 729, F3, 17) (dual of [729, 662, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(349, 729, F3, 13) (dual of [729, 680, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 24, F3, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(373, 613, F3, 2, 17) (dual of [(613, 2), 1153, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(373, 613, F3, 3, 17) (dual of [(613, 3), 1766, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(373, 613, F3, 4, 17) (dual of [(613, 4), 2379, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(373, 613, F3, 5, 17) (dual of [(613, 5), 2992, 18]-NRT-code) | [i] | ||
| 5 | Digital (56, 73, 613)-net over F3 | [i] | ||
| 6 | Linear OOA(373, 251, F3, 3, 17) (dual of [(251, 3), 680, 18]-NRT-code) | [i] | OOA Folding | |