Information on Result #684869
Linear OA(776, 16828, F7, 17) (dual of [16828, 16752, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(12) ⊂ 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(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(74, 20, F7, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,7)), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(776, 16828, F7, 2, 17) (dual of [(16828, 2), 33580, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(776, 16828, F7, 3, 17) (dual of [(16828, 3), 50408, 18]-NRT-code) | [i] | ||
| 3 | Digital (59, 76, 16828)-net over F7 | [i] | ||
| 4 | Linear OOA(776, 8414, F7, 2, 17) (dual of [(8414, 2), 16752, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(776, 5609, F7, 3, 17) (dual of [(5609, 3), 16751, 18]-NRT-code) | [i] | ||