Information on Result #2266580
Linear OA(3192, 6592, F3, 35) (dual of [6592, 6400, 36]-code), using 1 times code embedding in larger space based on linear OA(3191, 6591, F3, 35) (dual of [6591, 6400, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3192, 3769, F3, 2, 35) (dual of [(3769, 2), 7346, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3192, 3769, F3, 3, 35) (dual of [(3769, 3), 11115, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(3192, 3769, F3, 4, 35) (dual of [(3769, 4), 14884, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3192, 3769, F3, 5, 35) (dual of [(3769, 5), 18653, 36]-NRT-code) | [i] | ||
| 5 | Digital (157, 192, 3769)-net over F3 | [i] | ||
| 6 | Linear OOA(3192, 3296, F3, 2, 35) (dual of [(3296, 2), 6400, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3192, 1648, F3, 4, 35) (dual of [(1648, 4), 6400, 36]-NRT-code) | [i] | ||