Information on Result #677030
Linear OA(389, 747, F3, 21) (dual of [747, 658, 22]-code), using construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) based on
- linear OA(385, 729, F3, 22) (dual of [729, 644, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(373, 729, F3, 19) (dual of [729, 656, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(31, 15, F3, 1) (dual of [15, 14, 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(389, 626, F3, 2, 21) (dual of [(626, 2), 1163, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(389, 626, F3, 3, 21) (dual of [(626, 3), 1789, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(389, 626, F3, 4, 21) (dual of [(626, 4), 2415, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(389, 626, F3, 5, 21) (dual of [(626, 5), 3041, 22]-NRT-code) | [i] | ||
| 5 | Digital (68, 89, 626)-net over F3 | [i] | ||