Information on Result #2273591
Linear OA(4237, 16431, F4, 43) (dual of [16431, 16194, 44]-code), using 2 times code embedding in larger space based on linear OA(4235, 16429, F4, 43) (dual of [16429, 16194, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(36) [i] based on
- linear OA(4225, 16384, F4, 43) (dual of [16384, 16159, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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 OOA(4237, 15682, F4, 2, 43) (dual of [(15682, 2), 31127, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4237, 15682, F4, 3, 43) (dual of [(15682, 3), 46809, 44]-NRT-code) | [i] | ||
| 3 | Digital (194, 237, 15682)-net over F4 | [i] | ||
| 4 | Linear OOA(4237, 5477, F4, 3, 43) (dual of [(5477, 3), 16194, 44]-NRT-code) | [i] | OOA Folding | |