Information on Result #705699
Linear OA(3209, 741, F3, 53) (dual of [741, 532, 54]-code), using construction XX applied to C1 = C([313,364]), C2 = C([315,365]), C3 = C1 + C2 = C([315,364]), and C∩ = C1 ∩ C2 = C([313,365]) based on
- linear OA(3202, 728, F3, 52) (dual of [728, 526, 53]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {313,314,…,364}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3202, 728, F3, 51) (dual of [728, 526, 52]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {315,316,…,365}, and designed minimum distance d ≥ |I|+1 = 52 [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 = {313,314,…,365}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {315,316,…,364}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 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(30, 6, F3, 0) (dual of [6, 6, 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(3209, 370, F3, 2, 53) (dual of [(370, 2), 531, 54]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3209, 247, F3, 3, 53) (dual of [(247, 3), 532, 54]-NRT-code) | [i] | ||
| 3 | Linear OOA(3209, 185, F3, 4, 53) (dual of [(185, 4), 531, 54]-NRT-code) | [i] | ||
| 4 | Linear OOA(3209, 148, F3, 5, 53) (dual of [(148, 5), 531, 54]-NRT-code) | [i] | ||