Information on Result #705063
Linear OA(3156, 748, F3, 39) (dual of [748, 592, 40]-code), using construction XX applied to C1 = C([725,34]), C2 = C([0,36]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([725,36]) based on
- linear OA(3148, 728, F3, 38) (dual of [728, 580, 39]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,34}, and designed minimum distance d ≥ |I|+1 = 39 [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(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(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [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(3157, 749, F3, 39) (dual of [749, 592, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3157, 751, F3, 39) (dual of [751, 594, 40]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(3157, 750, F3, 39) (dual of [750, 593, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(3156, 374, F3, 2, 39) (dual of [(374, 2), 592, 40]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3156, 249, F3, 3, 39) (dual of [(249, 3), 591, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(3156, 187, F3, 4, 39) (dual of [(187, 4), 592, 40]-NRT-code) | [i] | ||