Information on Result #712802
Linear OA(777, 187, F7, 32) (dual of [187, 110, 33]-code), using construction XX applied to C1 = C([29,57]), C2 = C([35,60]), C3 = C1 + C2 = C([35,57]), and C∩ = C1 ∩ C2 = C([29,60]) based on
- linear OA(764, 171, F7, 29) (dual of [171, 107, 30]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {29,30,…,57}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(767, 171, F7, 26) (dual of [171, 104, 27]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {35,36,…,60}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(770, 171, F7, 32) (dual of [171, 101, 33]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {29,30,…,60}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(758, 171, F7, 23) (dual of [171, 113, 24]-code), using the BCH-code C(I) with length 171 | 73−1, defining interval I = {35,36,…,57}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using
- extended Reed–Solomon code RSe(3,7) [i]
- the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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 OA(778, 188, F7, 32) (dual of [188, 110, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(777, 93, F7, 2, 32) (dual of [(93, 2), 109, 33]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(777, 62, F7, 3, 32) (dual of [(62, 3), 109, 33]-NRT-code) | [i] | ||