Information on Result #677006
Linear OA(3122, 744, F3, 30) (dual of [744, 622, 31]-code), using construction XX applied to Ce(30) ⊂ Ce(27) ⊂ Ce(25) 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(3109, 729, F3, 28) (dual of [729, 620, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3103, 729, F3, 26) (dual of [729, 626, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
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(3122, 627, F3, 2, 30) (dual of [(627, 2), 1132, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3122, 627, F3, 3, 30) (dual of [(627, 3), 1759, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3122, 627, F3, 4, 30) (dual of [(627, 4), 2386, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3122, 627, F3, 5, 30) (dual of [(627, 5), 3013, 31]-NRT-code) | [i] | ||
| 5 | Digital (92, 122, 627)-net over F3 | [i] | ||