Information on Result #825140
Linear OOA(4194, 32776, F4, 2, 32) (dual of [(32776, 2), 65358, 33]-NRT-code), using OOA 2-folding based on linear OA(4194, 65552, F4, 32) (dual of [65552, 65358, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4194, 65553, F4, 32) (dual of [65553, 65359, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(29) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- 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(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(32) ⊂ Ce(29) [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(4194, 32776, F4, 3, 32) (dual of [(32776, 3), 98134, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (162, 194, 32776)-net over F4 | [i] | ||