Information on Result #705736
Linear OA(3218, 754, F3, 54) (dual of [754, 536, 55]-code), using construction XX applied to C1 = C([725,48]), C2 = C([0,51]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([725,51]) 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(3202, 728, F3, 52) (dual of [728, 526, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3214, 728, F3, 55) (dual of [728, 514, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,51}, and designed minimum distance d ≥ |I|+1 = 56 [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(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
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(3218, 377, F3, 2, 54) (dual of [(377, 2), 536, 55]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3218, 251, F3, 3, 54) (dual of [(251, 3), 535, 55]-NRT-code) | [i] | ||
| 3 | Linear OOA(3218, 188, F3, 4, 54) (dual of [(188, 4), 534, 55]-NRT-code) | [i] | ||