Information on Result #679750
Linear OA(4194, 4127, F4, 42) (dual of [4127, 3933, 43]-code), using construction X applied to Ce(41) ⊂ Ce(36) based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(47, 31, F4, 4) (dual of [31, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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(4195, 4128, F4, 42) (dual of [4128, 3933, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4195, 4129, F4, 42) (dual of [4129, 3934, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OA(4196, 4131, F4, 42) (dual of [4131, 3935, 43]-code) | [i] | ||
| 4 | Linear OOA(4194, 2063, F4, 2, 42) (dual of [(2063, 2), 3932, 43]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4194, 1375, F4, 3, 42) (dual of [(1375, 3), 3931, 43]-NRT-code) | [i] | ||