Information on Result #1218959
Digital (90, 104, 2398797)-net over F16, using (u, u+v)-construction based on
- digital (17, 24, 2055)-net over F16, using
- net defined by OOA [i] based on linear OOA(1624, 2055, F16, 10, 7) (dual of [(2055, 10), 20526, 8]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1624, 4111, F16, 2, 7) (dual of [(4111, 2), 8198, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1624, 4112, F16, 2, 7) (dual of [(4112, 2), 8200, 8]-NRT-code), using
- generalized (u, u+v)-construction [i] 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
- linear OOA(160, 257, F16, 2, 0) (dual of [(257, 2), 514, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(1624, 4112, F16, 2, 7) (dual of [(4112, 2), 8200, 8]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1624, 4111, F16, 2, 7) (dual of [(4111, 2), 8198, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1624, 2055, F16, 10, 7) (dual of [(2055, 10), 20526, 8]-NRT-code), using
- digital (66, 80, 2396742)-net over F16, using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, 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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.