Information on Result #895678
Linear OOA(4193, 4194311, F4, 2, 21) (dual of [(4194311, 2), 8388429, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(412, 10, F4, 2, 10) (dual of [(10, 2), 8, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,9P) [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- linear OOA(4181, 4194301, F4, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 2-folding [i] based on linear OA(4181, 8388602, F4, 21) (dual of [8388602, 8388421, 22]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4193, 4194311, F4, 3, 21) (dual of [(4194311, 3), 12582740, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (172, 193, 4194311)-net over F4 | [i] | ||
| 3 | Linear OOA(4193, 838862, F4, 22, 21) (dual of [(838862, 22), 18454771, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |