Information on Result #705154
Linear OA(3172, 753, F3, 43) (dual of [753, 581, 44]-code), using construction XX applied to C1 = C([725,37]), C2 = C([1,39]), C3 = C1 + C2 = C([1,37]), and C∩ = C1 ∩ C2 = C([725,39]) based on
- 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(3153, 728, F3, 39) (dual of [728, 575, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3166, 728, F3, 43) (dual of [728, 562, 44]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,39}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3147, 728, F3, 37) (dual of [728, 581, 38]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), using
- 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
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(3172, 376, F3, 2, 43) (dual of [(376, 2), 580, 44]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3172, 251, F3, 3, 43) (dual of [(251, 3), 581, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(3172, 188, F3, 4, 43) (dual of [(188, 4), 580, 44]-NRT-code) | [i] | ||