Information on Result #826455
Linear OOA(4246, 32782, F4, 2, 41) (dual of [(32782, 2), 65318, 42]-NRT-code), using OOA 2-folding based on linear OA(4246, 65564, F4, 41) (dual of [65564, 65318, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(4246, 65565, F4, 41) (dual of [65565, 65319, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
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(4246, 32782, F4, 2, 40) (dual of [(32782, 2), 65318, 41]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4246, 32782, F4, 3, 41) (dual of [(32782, 3), 98100, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (205, 246, 32782)-net over F4 | [i] | ||