Information on Result #2677578
Linear OOA(3203, 531456, F3, 3, 23) (dual of [(531456, 3), 1594165, 24]-NRT-code), using 31 times duplication based on linear OOA(3202, 531456, F3, 3, 23) (dual of [(531456, 3), 1594166, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3202, 1594368, F3, 23) (dual of [1594368, 1594166, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(3196, 1594323, F3, 23) (dual of [1594323, 1594127, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3157, 1594323, F3, 19) (dual of [1594323, 1594166, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [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(3203, 417346, F3, 4, 23) (dual of [(417346, 4), 1669181, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3203, 417346, F3, 5, 23) (dual of [(417346, 5), 2086527, 24]-NRT-code) | [i] | ||
| 3 | Digital (180, 203, 417346)-net over F3 | [i] | ||