Information on Result #712903
Linear OA(7100, 204, F7, 40) (dual of [204, 104, 41]-code), using construction XX applied to C1 = C([164,29]), C2 = C([0,32]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([164,32]) based on
- linear OA(782, 171, F7, 37) (dual of [171, 89, 38]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−7,−6,…,29}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(773, 171, F7, 33) (dual of [171, 98, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(788, 171, F7, 40) (dual of [171, 83, 41]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {−7,−6,…,32}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(767, 171, F7, 30) (dual of [171, 104, 31]-code), using the expurgated narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(710, 25, F7, 6) (dual of [25, 15, 7]-code), using
- an extension Ce(5) of the narrow-sense BCH-code C(I) with length 24 | 72−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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]
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(7100, 102, F7, 2, 40) (dual of [(102, 2), 104, 41]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7100, 68, F7, 3, 40) (dual of [(68, 3), 104, 41]-NRT-code) | [i] | ||