Information on Result #679783
Linear OA(4203, 4136, F4, 43) (dual of [4136, 3933, 44]-code), using construction X applied to Ce(42) ⊂ Ce(36) based on
- linear OA(4193, 4096, F4, 43) (dual of [4096, 3903, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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(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(4204, 4137, F4, 43) (dual of [4137, 3933, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4205, 4138, F4, 43) (dual of [4138, 3933, 44]-code) | [i] | ||
| 3 | Linear OA(4206, 4139, F4, 43) (dual of [4139, 3933, 44]-code) | [i] | ||
| 4 | Linear OA(4207, 4140, F4, 43) (dual of [4140, 3933, 44]-code) | [i] | ||
| 5 | Linear OA(4208, 4141, F4, 43) (dual of [4141, 3933, 44]-code) | [i] | ||
| 6 | Linear OOA(4203, 2068, F4, 2, 43) (dual of [(2068, 2), 3933, 44]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4203, 1378, F4, 3, 43) (dual of [(1378, 3), 3931, 44]-NRT-code) | [i] | ||