Information on Result #2273122
Linear OA(4248, 262202, F4, 35) (dual of [262202, 261954, 36]-code), using 3 times code embedding in larger space based on linear OA(4245, 262199, F4, 35) (dual of [262199, 261954, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(4235, 262144, F4, 35) (dual of [262144, 261909, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(410, 55, F4, 5) (dual of [55, 45, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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(4248, 140760, F4, 2, 35) (dual of [(140760, 2), 281272, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4248, 140760, F4, 3, 35) (dual of [(140760, 3), 422032, 36]-NRT-code) | [i] | ||
| 3 | Digital (213, 248, 140760)-net over F4 | [i] | ||