Information on Result #824421
Linear OOA(4161, 32772, F4, 2, 27) (dual of [(32772, 2), 65383, 28]-NRT-code), using OOA 2-folding based on linear OA(4161, 65544, F4, 27) (dual of [65544, 65383, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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(4161, 31815, F4, 3, 27) (dual of [(31815, 3), 95284, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (134, 161, 31815)-net over F4 | [i] | ||