Information on Result #705661
Linear OA(3212, 750, F3, 53) (dual of [750, 538, 54]-code), using construction XX applied to C1 = C([725,48]), C2 = C([0,49]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([725,49]) 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 = {−3,−2,…,48}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [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 = {−3,−2,…,49}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(3190, 728, F3, 49) (dual of [728, 538, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(34, 16, F3, 2) (dual of [16, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), 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(3212, 375, F3, 2, 53) (dual of [(375, 2), 538, 54]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3212, 250, F3, 3, 53) (dual of [(250, 3), 538, 54]-NRT-code) | [i] | ||
| 3 | Linear OOA(3212, 187, F3, 4, 53) (dual of [(187, 4), 536, 54]-NRT-code) | [i] | ||