Information on Result #906697
Linear OOA(1624, 4112, F16, 2, 7) (dual of [(4112, 2), 8200, 8]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(160, s, F16, 2, 0) for arbitrarily large s, using
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code) (see above)
- linear OOA(161, 257, F16, 2, 1) (dual of [(257, 2), 513, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(161, s, F16, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(161, s, F16, 2, 1) for arbitrarily large s, using
- linear OOA(161, 257, F16, 2, 1) (dual of [(257, 2), 513, 2]-NRT-code) (see above)
- linear OOA(161, 257, F16, 2, 1) (dual of [(257, 2), 513, 2]-NRT-code) (see above)
- linear OOA(161, 257, F16, 2, 1) (dual of [(257, 2), 513, 2]-NRT-code) (see above)
- linear OOA(163, 257, F16, 2, 2) (dual of [(257, 2), 511, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(163, 273, F16, 2, 2) (dual of [(273, 2), 543, 3]-NRT-code), using
- appending kth column [i] based on linear OA(163, 273, F16, 2) (dual of [273, 270, 3]-code), using
- Hamming code H(3,16) [i]
- appending kth column [i] based on linear OA(163, 273, F16, 2) (dual of [273, 270, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(163, 273, F16, 2, 2) (dual of [(273, 2), 543, 3]-NRT-code), using
- linear OOA(164, 257, F16, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
- linear OOA(1613, 257, F16, 2, 7) (dual of [(257, 2), 501, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(6,256) in PG(12,16)) for nets [i] based on digital (0, 7, 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(6,256) in PG(12,16)) for nets [i] based on digital (0, 7, 257)-net over F256, using
- extracting embedded OOA [i] based on digital (6, 13, 257)-net over F16, 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(1624, 2055, F16, 10, 7) (dual of [(2055, 10), 20526, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |