Information on Result #895612
Linear OOA(4167, 4194310, F4, 2, 18) (dual of [(4194310, 2), 8388453, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(410, 9, F4, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,8P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- extended algebraic-geometric NRT-code AGe(2;F,8P) [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- linear OOA(4157, 4194301, F4, 2, 18) (dual of [(4194301, 2), 8388445, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4157, 8388602, F4, 18) (dual of [8388602, 8388445, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- OOA 2-folding [i] based on linear OA(4157, 8388602, F4, 18) (dual of [8388602, 8388445, 19]-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(4167, 4194310, F4, 3, 18) (dual of [(4194310, 3), 12582763, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (149, 167, 4194310)-net over F4 | [i] | ||