Information on Result #679798
Linear OA(4137, 4136, F4, 28) (dual of [4136, 3999, 29]-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(410, 40, F4, 5) (dual of [40, 30, 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(4138, 4137, F4, 28) (dual of [4137, 3999, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4137, 2068, F4, 2, 28) (dual of [(2068, 2), 3999, 29]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4137, 1378, F4, 3, 28) (dual of [(1378, 3), 3997, 29]-NRT-code) | [i] | ||