Information on Result #705801
Linear OA(3216, 735, F3, 56) (dual of [735, 519, 57]-code), using construction XX applied to C1 = C([337,391]), C2 = C([336,388]), C3 = C1 + C2 = C([337,388]), and C∩ = C1 ∩ C2 = C([336,391]) based on
- linear OA(3211, 728, F3, 55) (dual of [728, 517, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,391}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(3208, 728, F3, 53) (dual of [728, 520, 54]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,388}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3214, 728, F3, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,391}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(3205, 728, F3, 52) (dual of [728, 523, 53]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {337,338,…,388}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-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 OOA(3216, 367, F3, 2, 56) (dual of [(367, 2), 518, 57]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3216, 245, F3, 3, 56) (dual of [(245, 3), 519, 57]-NRT-code) | [i] | ||