Information on Result #679943
Linear OA(4178, 4130, F4, 38) (dual of [4130, 3952, 39]-code), using construction XX applied to Ce(37) ⊂ Ce(32) ⊂ Ce(30) 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(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(47, 32, F4, 4) (dual of [32, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(4179, 4131, F4, 38) (dual of [4131, 3952, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4180, 4132, F4, 38) (dual of [4132, 3952, 39]-code) | [i] | ||
| 3 | Linear OA(4181, 4133, F4, 38) (dual of [4133, 3952, 39]-code) | [i] | ||
| 4 | Linear OOA(4178, 2065, F4, 2, 38) (dual of [(2065, 2), 3952, 39]-NRT-code) | [i] | OOA Folding | |