Information on Result #705100
Linear OA(3163, 747, F3, 41) (dual of [747, 584, 42]-code), using construction XX applied to C1 = C([725,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([725,37]) based on
- linear OA(3154, 728, F3, 40) (dual of [728, 574, 41]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,36}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3148, 728, F3, 38) (dual of [728, 580, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(3160, 728, F3, 41) (dual of [728, 568, 42]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,37}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- 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(3163, 373, F3, 2, 41) (dual of [(373, 2), 583, 42]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3163, 249, F3, 3, 41) (dual of [(249, 3), 584, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3163, 186, F3, 4, 41) (dual of [(186, 4), 581, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3163, 149, F3, 5, 41) (dual of [(149, 5), 582, 42]-NRT-code) | [i] | ||