Information on Result #2271515
Linear OA(4117, 65580, F4, 18) (dual of [65580, 65463, 19]-code), using 5 times code embedding in larger space based on linear OA(4112, 65575, F4, 18) (dual of [65575, 65463, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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(4117, 52511, F4, 2, 18) (dual of [(52511, 2), 104905, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4117, 52511, F4, 3, 18) (dual of [(52511, 3), 157416, 19]-NRT-code) | [i] | ||
| 3 | Digital (99, 117, 52511)-net over F4 | [i] | ||