Information on Result #825888
Linear OOA(4218, 32772, F4, 2, 37) (dual of [(32772, 2), 65326, 38]-NRT-code), using OOA 2-folding based on linear OA(4218, 65544, F4, 37) (dual of [65544, 65326, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(4218, 65545, F4, 37) (dual of [65545, 65327, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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(36) ⊂ Ce(34) [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(4218, 30117, F4, 3, 37) (dual of [(30117, 3), 90133, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (181, 218, 30117)-net over F4 | [i] | ||