Information on Result #679799
Linear OA(4131, 4136, F4, 27) (dual of [4136, 4005, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
- linear OA(4121, 4096, F4, 27) (dual of [4096, 3975, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(4132, 4137, F4, 27) (dual of [4137, 4005, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4133, 4138, F4, 27) (dual of [4138, 4005, 28]-code) | [i] | ||
| 3 | Linear OA(4134, 4139, F4, 27) (dual of [4139, 4005, 28]-code) | [i] | ||
| 4 | Linear OA(4135, 4140, F4, 27) (dual of [4140, 4005, 28]-code) | [i] | ||
| 5 | Linear OA(4136, 4141, F4, 27) (dual of [4141, 4005, 28]-code) | [i] | ||
| 6 | Linear OA(4132, 4138, F4, 27) (dual of [4138, 4006, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(4131, 2068, F4, 2, 27) (dual of [(2068, 2), 4005, 28]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4131, 1378, F4, 3, 27) (dual of [(1378, 3), 4003, 28]-NRT-code) | [i] | ||