Information on Result #704427
Linear OA(3103, 753, F3, 25) (dual of [753, 650, 26]-code), using construction XX applied to C1 = C([725,19]), C2 = C([1,21]), C3 = C1 + C2 = C([1,19]), and C∩ = C1 ∩ C2 = C([725,21]) based on
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,19}, and designed minimum distance d ≥ |I|+1 = 24 [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(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(378, 728, F3, 19) (dual of [728, 650, 20]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(3103, 596, F3, 2, 25) (dual of [(596, 2), 1089, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3103, 596, F3, 3, 25) (dual of [(596, 3), 1685, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(3103, 596, F3, 4, 25) (dual of [(596, 4), 2281, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(3103, 596, F3, 5, 25) (dual of [(596, 5), 2877, 26]-NRT-code) | [i] | ||
| 5 | Digital (78, 103, 596)-net over F3 | [i] | ||
| 6 | Linear OOA(3103, 376, F3, 2, 25) (dual of [(376, 2), 649, 26]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3103, 251, F3, 3, 25) (dual of [(251, 3), 650, 26]-NRT-code) | [i] | ||
| 8 | Linear OOA(3103, 188, F3, 4, 25) (dual of [(188, 4), 649, 26]-NRT-code) | [i] | ||