Information on Result #704511
Linear OA(3115, 759, F3, 27) (dual of [759, 644, 28]-code), using construction XX applied to C1 = C([725,21]), C2 = C([1,24]), C3 = C1 + C2 = C([1,21]), and C∩ = C1 ∩ C2 = C([725,24]) based on
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,21}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(396, 728, F3, 24) (dual of [728, 632, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,24}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(384, 728, F3, 21) (dual of [728, 644, 22]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), using
- 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
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(3115, 253, F3, 3, 27) (dual of [(253, 3), 644, 28]-NRT-code) | [i] | OOA Folding | |