Information on Result #678751
Linear OA(4227, 65586, F4, 36) (dual of [65586, 65359, 37]-code), using construction X applied to Ce(36) ⊂ Ce(29) 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(410, 50, F4, 5) (dual of [50, 40, 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 OA(4228, 65587, F4, 36) (dual of [65587, 65359, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4227, 45292, F4, 2, 36) (dual of [(45292, 2), 90357, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4227, 45292, F4, 3, 36) (dual of [(45292, 3), 135649, 37]-NRT-code) | [i] | ||
| 4 | Digital (191, 227, 45292)-net over F4 | [i] | ||
| 5 | Linear OOA(4227, 32793, F4, 2, 36) (dual of [(32793, 2), 65359, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4227, 21862, F4, 3, 36) (dual of [(21862, 3), 65359, 37]-NRT-code) | [i] | ||