Information on Result #823403
Linear OOA(4105, 32772, F4, 2, 18) (dual of [(32772, 2), 65439, 19]-NRT-code), using OOA 2-folding based on linear OA(4105, 65544, F4, 18) (dual of [65544, 65439, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [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(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(4107, 32773, F4, 2, 18) (dual of [(32773, 2), 65439, 19]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4106, 32772, F4, 2, 18) (dual of [(32772, 2), 65438, 19]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4105, 29149, F4, 3, 18) (dual of [(29149, 3), 87342, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (87, 105, 29149)-net over F4 | [i] | ||