Information on Result #713416
Linear OA(741, 349, F7, 16) (dual of [349, 308, 17]-code), using construction XX applied to C1 = C([43,57]), C2 = C([45,58]), C3 = C1 + C2 = C([45,57]), and C∩ = C1 ∩ C2 = C([43,58]) 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 = {45,46,…,58}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {43,44,…,58}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(734, 342, F7, 13) (dual of [342, 308, 14]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {45,46,…,57}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- 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(741, 254, F7, 2, 16) (dual of [(254, 2), 467, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(741, 254, F7, 3, 16) (dual of [(254, 3), 721, 17]-NRT-code) | [i] | ||
| 3 | Digital (25, 41, 254)-net over F7 | [i] | ||
| 4 | Linear OOA(741, 174, F7, 2, 16) (dual of [(174, 2), 307, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(741, 116, F7, 3, 16) (dual of [(116, 3), 307, 17]-NRT-code) | [i] | ||