Information on Result #679218
Linear OA(4178, 16442, F4, 31) (dual of [16442, 16264, 32]-code), using construction X applied to Ce(30) ⊂ Ce(22) based on
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-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(4179, 16443, F4, 31) (dual of [16443, 16264, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4179, 16444, F4, 31) (dual of [16444, 16265, 32]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(4178, 8221, F4, 2, 31) (dual of [(8221, 2), 16264, 32]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4178, 5480, F4, 3, 31) (dual of [(5480, 3), 16262, 32]-NRT-code) | [i] | ||