Information on Result #713120
Linear OA(7106, 190, F7, 46) (dual of [190, 84, 47]-code), using construction XX applied to C1 = C([168,39]), C2 = C([1,42]), C3 = C1 + C2 = C([1,39]), and C∩ = C1 ∩ C2 = C([168,42]) based on
- linear OA(794, 171, F7, 43) (dual of [171, 77, 44]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,39}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(793, 171, F7, 42) (dual of [171, 78, 43]-code), using the narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(7100, 171, F7, 46) (dual of [171, 71, 47]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,42}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(787, 171, F7, 39) (dual of [171, 84, 40]-code), using the narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(74, 11, F7, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,7)), using
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
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 OA(7107, 191, F7, 46) (dual of [191, 84, 47]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7106, 95, F7, 2, 46) (dual of [(95, 2), 84, 47]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(7106, 63, F7, 3, 46) (dual of [(63, 3), 83, 47]-NRT-code) | [i] | ||