Information on Result #1011722
Linear OOA(450, large, F4, 3, 5), using (u, u+v)-construction based on
- linear OOA(42, 5, F4, 3, 2) (dual of [(5, 3), 13, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;13,4) [i]
- linear OOA(448, 8388602, F4, 3, 5) (dual of [(8388602, 3), 25165758, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(448, large, F4, 2, 5), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(41, 2097152, F4, 2, 1) (dual of [(2097152, 2), 4194303, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(41, s, F4, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(41, s, F4, 2, 1) for arbitrarily large s, using
- linear OOA(41, 2097152, F4, 2, 1) (dual of [(2097152, 2), 4194303, 2]-NRT-code) (see above)
- linear OOA(412, 2097152, F4, 2, 2) (dual of [(2097152, 2), 4194292, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(412, 5592405, F4, 2, 2) (dual of [(5592405, 2), 11184798, 3]-NRT-code), using
- appending kth column [i] based on linear OA(412, 5592405, F4, 2) (dual of [5592405, 5592393, 3]-code), using
- Hamming code H(12,4) [i]
- appending kth column [i] based on linear OA(412, 5592405, F4, 2) (dual of [5592405, 5592393, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(412, 5592405, F4, 2, 2) (dual of [(5592405, 2), 11184798, 3]-NRT-code), using
- linear OOA(434, 2097152, F4, 2, 5) (dual of [(2097152, 2), 4194270, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- OOA 2-folding [i] based on linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using
- linear OOA(41, 2097152, F4, 2, 1) (dual of [(2097152, 2), 4194303, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(448, large, F4, 2, 5), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(450, large, F4, 3, 4) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(450, large, F4, 3, 3) | [i] | ||