Information on Result #679797
Linear OA(4140, 4139, F4, 29) (dual of [4139, 3999, 30]-code), using construction X applied to Ce(28) ⊂ Ce(21) based on
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(497, 4096, F4, 22) (dual of [4096, 3999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(413, 43, F4, 6) (dual of [43, 30, 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 OA(4141, 4140, F4, 29) (dual of [4140, 3999, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4142, 4141, F4, 29) (dual of [4141, 3999, 30]-code) | [i] | ||
| 3 | Linear OA(4139, 4138, F4, 28) (dual of [4138, 3999, 29]-code) | [i] | Truncation | |
| 4 | Linear OA(4141, 4141, F4, 29) (dual of [4141, 4000, 30]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(4140, 2069, F4, 2, 29) (dual of [(2069, 2), 3998, 30]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4140, 1379, F4, 3, 29) (dual of [(1379, 3), 3997, 30]-NRT-code) | [i] | ||