Information on Result #705201
Linear OA(3168, 748, F3, 42) (dual of [748, 580, 43]-code), using construction XX applied to C1 = C([725,37]), C2 = C([0,39]), C3 = C1 + C2 = C([0,37]), 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(3154, 728, F3, 40) (dual of [728, 574, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [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(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(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
- 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 (see above)
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 OA(3169, 749, F3, 42) (dual of [749, 580, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3168, 374, F3, 2, 42) (dual of [(374, 2), 580, 43]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3168, 249, F3, 3, 42) (dual of [(249, 3), 579, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3168, 187, F3, 4, 42) (dual of [(187, 4), 580, 43]-NRT-code) | [i] | ||