Information on Result #714119
Linear OA(7108, 362, F7, 40) (dual of [362, 254, 41]-code), using construction XX applied to C1 = C([338,33]), C2 = C([0,35]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([338,35]) based on
- linear OA(7100, 342, F7, 38) (dual of [342, 242, 39]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−4,−3,…,33}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(791, 342, F7, 36) (dual of [342, 251, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(7103, 342, F7, 40) (dual of [342, 239, 41]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−4,−3,…,35}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(788, 342, F7, 34) (dual of [342, 254, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(74, 16, F7, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,7)), using
- linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), 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(7108, 181, F7, 2, 40) (dual of [(181, 2), 254, 41]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7108, 120, F7, 3, 40) (dual of [(120, 3), 252, 41]-NRT-code) | [i] | ||