Information on Result #813182
Linear OOA(3128, 265742, F3, 2, 15) (dual of [(265742, 2), 531356, 16]-NRT-code), using OOA 2-folding based on linear OA(3128, 531484, F3, 15) (dual of [531484, 531356, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3127, 531483, F3, 15) (dual of [531483, 531356, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(385, 531441, F3, 11) (dual of [531441, 531356, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
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(3128, 265742, F3, 3, 15) (dual of [(265742, 3), 797098, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3128, 265742, F3, 4, 15) (dual of [(265742, 4), 1062840, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(3128, 265742, F3, 5, 15) (dual of [(265742, 5), 1328582, 16]-NRT-code) | [i] | ||
| 4 | Digital (113, 128, 265742)-net over F3 | [i] | ||