Information on Result #824845
Linear OOA(4182, 32782, F4, 2, 30) (dual of [(32782, 2), 65382, 31]-NRT-code), using OOA 2-folding based on linear OA(4182, 65564, F4, 30) (dual of [65564, 65382, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 65565, F4, 30) (dual of [65565, 65383, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(29) ⊂ Ce(25) [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(4182, 32782, F4, 3, 30) (dual of [(32782, 3), 98164, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (152, 182, 32782)-net over F4 | [i] | ||