Information on Result #2273290
Linear OA(4240, 65591, F4, 38) (dual of [65591, 65351, 39]-code), using 2 times code embedding in larger space based on linear OA(4238, 65589, F4, 38) (dual of [65589, 65351, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(413, 53, F4, 6) (dual of [53, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), 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(4240, 47245, F4, 2, 38) (dual of [(47245, 2), 94250, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4240, 47245, F4, 3, 38) (dual of [(47245, 3), 141495, 39]-NRT-code) | [i] | ||
| 3 | Digital (202, 240, 47245)-net over F4 | [i] | ||