Information on Result #679752
Linear OA(4176, 4127, F4, 38) (dual of [4127, 3951, 39]-code), using construction X applied to Ce(37) ⊂ Ce(32) based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(4177, 4128, F4, 38) (dual of [4128, 3951, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4176, 3992, F4, 2, 38) (dual of [(3992, 2), 7808, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4176, 3992, F4, 3, 38) (dual of [(3992, 3), 11800, 39]-NRT-code) | [i] | ||
| 4 | Digital (138, 176, 3992)-net over F4 | [i] | ||
| 5 | Linear OA(4177, 4129, F4, 38) (dual of [4129, 3952, 39]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4178, 4131, F4, 38) (dual of [4131, 3953, 39]-code) | [i] | ||
| 7 | Linear OA(4179, 4133, F4, 38) (dual of [4133, 3954, 39]-code) | [i] | ||
| 8 | Linear OOA(4176, 2063, F4, 2, 38) (dual of [(2063, 2), 3950, 39]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(4176, 1375, F4, 3, 38) (dual of [(1375, 3), 3949, 39]-NRT-code) | [i] | ||