Information on Result #714156
Linear OA(7110, 352, F7, 42) (dual of [352, 242, 43]-code), using construction XX applied to C1 = C([340,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([340,39]) based on
- linear OA(7106, 342, F7, 41) (dual of [342, 236, 42]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(7103, 342, F7, 40) (dual of [342, 239, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(7109, 342, F7, 42) (dual of [342, 233, 43]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,39}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(7100, 342, F7, 39) (dual of [342, 242, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-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(7110, 176, F7, 2, 42) (dual of [(176, 2), 242, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7110, 117, F7, 3, 42) (dual of [(117, 3), 241, 43]-NRT-code) | [i] | ||