Information on Result #2677287
Linear OOA(3178, 531456, F3, 3, 20) (dual of [(531456, 3), 1594190, 21]-NRT-code), using 32 times duplication based on linear OOA(3176, 531456, F3, 3, 20) (dual of [(531456, 3), 1594192, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3176, 1594368, F3, 20) (dual of [1594368, 1594192, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-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(19) ⊂ Ce(15) [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(3178, 531456, F3, 4, 20) (dual of [(531456, 4), 2125646, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3178, 531456, F3, 5, 20) (dual of [(531456, 5), 2657102, 21]-NRT-code) | [i] | ||
| 3 | Digital (158, 178, 531456)-net over F3 | [i] | ||