Information on Result #679183
Linear OA(4231, 16432, F4, 42) (dual of [16432, 16201, 43]-code), using construction X applied to Ce(41) ⊂ Ce(34) based on
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(413, 48, F4, 6) (dual of [48, 35, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-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(4232, 16433, F4, 42) (dual of [16433, 16201, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4233, 16434, F4, 42) (dual of [16434, 16201, 43]-code) | [i] | ||
| 3 | Linear OA(4233, 16435, F4, 42) (dual of [16435, 16202, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(4231, 8216, F4, 2, 42) (dual of [(8216, 2), 16201, 43]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4231, 5477, F4, 3, 42) (dual of [(5477, 3), 16200, 43]-NRT-code) | [i] | ||