Information on Result #2272894
Linear OA(4180, 16430, F4, 32) (dual of [16430, 16250, 33]-code), using 1 times code embedding in larger space based on linear OA(4179, 16429, F4, 32) (dual of [16429, 16250, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 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(4180, 15678, F4, 2, 32) (dual of [(15678, 2), 31176, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4180, 15678, F4, 3, 32) (dual of [(15678, 3), 46854, 33]-NRT-code) | [i] | ||
| 3 | Digital (148, 180, 15678)-net over F4 | [i] | ||
| 4 | Linear OOA(4180, 8215, F4, 2, 32) (dual of [(8215, 2), 16250, 33]-NRT-code) | [i] | OOA Folding | |