Information on Result #713515
Linear OA(767, 372, F7, 23) (dual of [372, 305, 24]-code), using construction XX applied to C1 = C([45,64]), C2 = C([42,58]), C3 = C1 + C2 = C([45,58]), and C∩ = C1 ∩ C2 = C([42,64]) based on
- linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {45,46,…,64}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {42,43,…,58}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(758, 342, F7, 23) (dual of [342, 284, 24]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {42,43,…,64}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(737, 342, F7, 14) (dual of [342, 305, 15]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {45,46,…,58}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(77, 22, F7, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- 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(768, 373, F7, 23) (dual of [373, 305, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(767, 186, F7, 2, 23) (dual of [(186, 2), 305, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(767, 124, F7, 3, 23) (dual of [(124, 3), 305, 24]-NRT-code) | [i] | ||