Information on Result #704876
Linear OA(3148, 753, F3, 37) (dual of [753, 605, 38]-code), using construction XX applied to C1 = C([725,31]), C2 = C([1,33]), C3 = C1 + C2 = C([1,31]), and C∩ = C1 ∩ C2 = C([725,33]) based on
- linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,31}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3129, 728, F3, 33) (dual of [728, 599, 34]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,33}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3123, 728, F3, 31) (dual of [728, 605, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(3148, 376, F3, 2, 37) (dual of [(376, 2), 604, 38]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3148, 251, F3, 3, 37) (dual of [(251, 3), 605, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3148, 188, F3, 4, 37) (dual of [(188, 4), 604, 38]-NRT-code) | [i] | ||