Information on Result #713137
Linear OA(7103, 183, F7, 46) (dual of [183, 80, 47]-code), using construction XX applied to C1 = C([168,40]), C2 = C([0,42]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([168,42]) based on
- linear OA(797, 171, F7, 44) (dual of [171, 74, 45]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−3,−2,…,40}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(794, 171, F7, 43) (dual of [171, 77, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [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(791, 171, F7, 41) (dual of [171, 80, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [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, 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(7103, 91, F7, 2, 46) (dual of [(91, 2), 79, 47]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7103, 61, F7, 3, 46) (dual of [(61, 3), 80, 47]-NRT-code) | [i] | ||