Information on Result #705917
Linear OA(3243, 748, F3, 63) (dual of [748, 505, 64]-code), using construction XX applied to C1 = C([725,58]), C2 = C([0,60]), C3 = C1 + C2 = C([0,58]), and C∩ = C1 ∩ C2 = C([725,60]) based on
- linear OA(3235, 728, F3, 62) (dual of [728, 493, 63]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,58}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(3229, 728, F3, 61) (dual of [728, 499, 62]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,60], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(3241, 728, F3, 64) (dual of [728, 487, 65]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,60}, and designed minimum distance d ≥ |I|+1 = 65 [i]
- linear OA(3223, 728, F3, 59) (dual of [728, 505, 60]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,58], and designed minimum distance d ≥ |I|+1 = 60 [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(3244, 749, F3, 63) (dual of [749, 505, 64]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3243, 374, F3, 2, 63) (dual of [(374, 2), 505, 64]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3243, 249, F3, 3, 63) (dual of [(249, 3), 504, 64]-NRT-code) | [i] | ||
| 4 | Linear OOA(3243, 187, F3, 4, 63) (dual of [(187, 4), 505, 64]-NRT-code) | [i] | ||