Information on Result #713306
Linear OA(748, 369, F7, 16) (dual of [369, 321, 17]-code), using construction XX applied to C1 = C([43,56]), C2 = C([49,58]), C3 = C1 + C2 = C([49,56]), and C∩ = C1 ∩ C2 = C([43,58]) based on
- linear OA(736, 342, F7, 14) (dual of [342, 306, 15]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {43,44,…,56}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,58}, and designed minimum distance d ≥ |I|+1 = 11 [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(721, 342, F7, 8) (dual of [342, 321, 9]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,56}, and designed minimum distance d ≥ |I|+1 = 9 [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(71, 5, F7, 1) (dual of [5, 4, 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
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(748, 184, F7, 2, 16) (dual of [(184, 2), 320, 17]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(748, 123, F7, 3, 16) (dual of [(123, 3), 321, 17]-NRT-code) | [i] | ||