Information on Result #676754
Linear OA(3126, 758, F3, 30) (dual of [758, 632, 31]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(397, 729, F3, 25) (dual of [729, 632, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(38, 29, F3, 4) (dual of [29, 21, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3126, 737, F3, 2, 30) (dual of [(737, 2), 1348, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3126, 737, F3, 3, 30) (dual of [(737, 3), 2085, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3126, 737, F3, 4, 30) (dual of [(737, 4), 2822, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3126, 737, F3, 5, 30) (dual of [(737, 5), 3559, 31]-NRT-code) | [i] | ||
| 5 | Digital (96, 126, 737)-net over F3 | [i] | ||