Information on Result #684881
Linear OA(736, 16828, F7, 8) (dual of [16828, 16792, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(716, 16807, F7, 4) (dual of [16807, 16791, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(711, 16807, F7, 3) (dual of [16807, 16796, 4]-code or 16807-cap in PG(10,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(736, 16828, F7, 2, 8) (dual of [(16828, 2), 33620, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(736, 16828, F7, 3, 8) (dual of [(16828, 3), 50448, 9]-NRT-code) | [i] | ||
| 3 | Digital (28, 36, 16828)-net over F7 | [i] | ||
| 4 | Linear OOA(736, 8414, F7, 2, 8) (dual of [(8414, 2), 16792, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(736, 5609, F7, 3, 8) (dual of [(5609, 3), 16791, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(736, 4207, F7, 8, 8) (dual of [(4207, 8), 33620, 9]-NRT-code) | [i] | OA Folding and Stacking | |