Information on Result #714143
Linear OA(7109, 357, F7, 41) (dual of [357, 248, 42]-code), using construction XX applied to C1 = C([339,35]), C2 = C([0,37]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([339,37]) based on
- linear OA(7100, 342, F7, 39) (dual of [342, 242, 40]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−3,−2,…,35}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(797, 342, F7, 38) (dual of [342, 245, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- 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 = {−3,−2,…,37}, and designed minimum distance d ≥ |I|+1 = 42 [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(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]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [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 OOA(7109, 119, F7, 3, 41) (dual of [(119, 3), 248, 42]-NRT-code) | [i] | OOA Folding | |