Information on Result #898320
Linear OOA(1672, 524547, F16, 2, 13) (dual of [(524547, 2), 1049022, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(1611, 257, F16, 2, 6) (dual of [(257, 2), 503, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 11, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(5,256) in PG(10,16)) for nets [i] based on digital (0, 6, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base reduction for projective spaces (embedding PG(5,256) in PG(10,16)) for nets [i] based on digital (0, 6, 257)-net over F256, using
- extracting embedded OOA [i] based on digital (5, 11, 257)-net over F16, using
- linear OOA(1661, 524290, F16, 2, 13) (dual of [(524290, 2), 1048519, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1661, 1048580, F16, 13) (dual of [1048580, 1048519, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(1661, 1048581, F16, 13) (dual of [1048581, 1048520, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(1661, 1048581, F16, 13) (dual of [1048581, 1048520, 14]-code), using
- OOA 2-folding [i] based on linear OA(1661, 1048580, F16, 13) (dual of [1048580, 1048519, 14]-code), using
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(1672, 174848, F16, 14, 13) (dual of [(174848, 14), 2447800, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |