Information on Result #684834
Linear OA(773, 16839, F7, 16) (dual of [16839, 16766, 17]-code), using construction X applied to Ce(15) ⊂ Ce(9) based on
- linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-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 OA(774, 16840, F7, 16) (dual of [16840, 16766, 17]-code) | [i] | Code Embedding in Larger Space | |
2 | Linear OA(775, 16841, F7, 16) (dual of [16841, 16766, 17]-code) | [i] | ||
3 | Linear OA(776, 16842, F7, 16) (dual of [16842, 16766, 17]-code) | [i] | ||
4 | Linear OOA(773, 16839, F7, 2, 16) (dual of [(16839, 2), 33605, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
5 | Linear OOA(773, 16839, F7, 3, 16) (dual of [(16839, 3), 50444, 17]-NRT-code) | [i] | ||
6 | Digital (57, 73, 16839)-net over F7 | [i] | ||
7 | Linear OA(774, 16841, F7, 16) (dual of [16841, 16767, 17]-code) | [i] | Construction X with Varšamov Bound | |
8 | Linear OOA(773, 8419, F7, 2, 16) (dual of [(8419, 2), 16765, 17]-NRT-code) | [i] | OOA Folding | |
9 | Linear OOA(773, 5613, F7, 3, 16) (dual of [(5613, 3), 16766, 17]-NRT-code) | [i] |