Information on Result #713128
Linear OA(7102, 182, F7, 45) (dual of [182, 80, 46]-code), using construction XX applied to C1 = C([14,57]), C2 = C([17,58]), C3 = C1 + C2 = C([17,57]), and C∩ = C1 ∩ C2 = C([14,58]) 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 = {14,15,…,57}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(794, 171, F7, 42) (dual of [171, 77, 43]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {17,18,…,58}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(7100, 171, F7, 45) (dual of [171, 71, 46]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {14,15,…,58}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(791, 171, F7, 41) (dual of [171, 80, 42]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {17,18,…,57}, 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(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(7102, 91, F7, 2, 45) (dual of [(91, 2), 80, 46]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7102, 60, F7, 3, 45) (dual of [(60, 3), 78, 46]-NRT-code) | [i] | ||