Information on Result #684819
Linear OA(777, 16833, F7, 17) (dual of [16833, 16756, 18]-code), using construction X applied to Ce(16) ⊂ Ce(11) based on
- linear OA(771, 16807, F7, 17) (dual of [16807, 16736, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(777, 16833, F7, 2, 17) (dual of [(16833, 2), 33589, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(777, 16833, F7, 3, 17) (dual of [(16833, 3), 50422, 18]-NRT-code) | [i] | ||
| 3 | Digital (60, 77, 16833)-net over F7 | [i] | ||
| 4 | Linear OOA(777, 8416, F7, 2, 17) (dual of [(8416, 2), 16755, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(777, 5611, F7, 3, 17) (dual of [(5611, 3), 16756, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(777, 2104, F7, 17, 17) (dual of [(2104, 17), 35691, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |