Information on Result #895716
Linear OOA(4221, 4194377, F4, 2, 22) (dual of [(4194377, 2), 8388533, 23]-NRT-code), using (u, u+v)-construction based on
- linear OOA(428, 76, F4, 2, 11) (dual of [(76, 2), 124, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (17, 28, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 14, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- trace code for nets [i] based on digital (3, 14, 38)-net over F16, using
- extracting embedded OOA [i] based on digital (17, 28, 76)-net over F4, using
- linear OOA(4193, 4194301, F4, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-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(4222, 4194377, F4, 2, 22) (dual of [(4194377, 2), 8388532, 23]-NRT-code) | [i] | OOA Duplication | |