Information on Result #704470
Linear OA(3122, 778, F3, 27) (dual of [778, 656, 28]-code), using construction XX applied to C1 = C([724,18]), C2 = C([1,22]), C3 = C1 + C2 = C([1,18]), and C∩ = C1 ∩ C2 = C([724,22]) 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 = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(390, 728, F3, 22) (dual of [728, 638, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3109, 728, F3, 27) (dual of [728, 619, 28]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(372, 728, F3, 18) (dual of [728, 656, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(36, 24, F3, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3122, 389, F3, 2, 27) (dual of [(389, 2), 656, 28]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3122, 259, F3, 3, 27) (dual of [(259, 3), 655, 28]-NRT-code) | [i] | ||