Information on Result #2272755
Linear OA(4194, 65601, F4, 30) (dual of [65601, 65407, 31]-code), using 1 times code embedding in larger space based on linear OA(4193, 65600, F4, 30) (dual of [65600, 65407, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
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(4194, 53164, F4, 2, 30) (dual of [(53164, 2), 106134, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4194, 53164, F4, 3, 30) (dual of [(53164, 3), 159298, 31]-NRT-code) | [i] | ||
| 3 | Digital (164, 194, 53164)-net over F4 | [i] | ||
| 4 | Linear OOA(4194, 21867, F4, 3, 30) (dual of [(21867, 3), 65407, 31]-NRT-code) | [i] | OOA Folding | |