Information on Result #684820
Linear OA(772, 16833, F7, 16) (dual of [16833, 16761, 17]-code), using construction X applied to Ce(15) ⊂ Ce(10) 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(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(76, 26, F7, 4) (dual of [26, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-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(772, 16833, F7, 2, 16) (dual of [(16833, 2), 33594, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(772, 16833, F7, 3, 16) (dual of [(16833, 3), 50427, 17]-NRT-code) | [i] | ||
| 3 | Digital (56, 72, 16833)-net over F7 | [i] | ||
| 4 | Linear OOA(772, 8416, F7, 2, 16) (dual of [(8416, 2), 16760, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(772, 5611, F7, 3, 16) (dual of [(5611, 3), 16761, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(772, 2104, F7, 16, 16) (dual of [(2104, 16), 33592, 17]-NRT-code) | [i] | OA Folding and Stacking | |