Information on Result #677986
Linear OA(4242, 4194358, F4, 29) (dual of [4194358, 4194116, 30]-code), using construction X applied to Ce(28) ⊂ Ce(22) based on
- linear OA(4232, 4194304, F4, 29) (dual of [4194304, 4194072, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(410, 54, F4, 5) (dual of [54, 44, 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(4243, 4194359, F4, 29) (dual of [4194359, 4194116, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4244, 4194360, F4, 29) (dual of [4194360, 4194116, 30]-code) | [i] | ||
| 3 | Linear OA(4241, 4194357, F4, 28) (dual of [4194357, 4194116, 29]-code) | [i] | Truncation | |
| 4 | Linear OOA(4242, 2097179, F4, 2, 29) (dual of [(2097179, 2), 4194116, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4242, 1398119, F4, 3, 29) (dual of [(1398119, 3), 4194115, 30]-NRT-code) | [i] | ||