Information on Result #713433
Linear OA(746, 357, F7, 17) (dual of [357, 311, 18]-code), using construction XX applied to C1 = C([43,57]), C2 = C([46,59]), C3 = C1 + C2 = C([46,57]), and C∩ = C1 ∩ C2 = C([43,59]) based on
- linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {43,44,…,57}, and designed minimum distance d ≥ |I|+1 = 16 [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 = {46,47,…,59}, and designed minimum distance d ≥ |I|+1 = 15 [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 = {43,44,…,59}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(731, 342, F7, 12) (dual of [342, 311, 13]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {46,47,…,57}, and designed minimum distance d ≥ |I|+1 = 13 [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, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [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(747, 359, F7, 17) (dual of [359, 312, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(746, 178, F7, 2, 17) (dual of [(178, 2), 310, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(746, 119, F7, 3, 17) (dual of [(119, 3), 311, 18]-NRT-code) | [i] | ||