Information on Result #2273214
Linear OA(4231, 65590, F4, 37) (dual of [65590, 65359, 38]-code), using 1 times code embedding in larger space based on linear OA(4230, 65589, F4, 37) (dual of [65589, 65359, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(29) [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(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(4231, 41903, F4, 2, 37) (dual of [(41903, 2), 83575, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4231, 41903, F4, 3, 37) (dual of [(41903, 3), 125478, 38]-NRT-code) | [i] | ||
| 3 | Digital (194, 231, 41903)-net over F4 | [i] | ||
| 4 | Linear OOA(4231, 32795, F4, 2, 37) (dual of [(32795, 2), 65359, 38]-NRT-code) | [i] | OOA Folding | |