Information on Result #679181
Linear OA(4242, 16429, F4, 44) (dual of [16429, 16187, 45]-code), using construction X applied to Ce(44) ⊂ Ce(37) based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4197, 16384, F4, 38) (dual of [16384, 16187, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 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, 16430, F4, 44) (dual of [16430, 16187, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4244, 16432, F4, 44) (dual of [16432, 16188, 45]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(4242, 8214, F4, 2, 44) (dual of [(8214, 2), 16186, 45]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4242, 5476, F4, 3, 44) (dual of [(5476, 3), 16186, 45]-NRT-code) | [i] | ||