Information on Result #1186602
Digital (157, 173, 1048639)-net over F4, using net defined by OOA based on linear OOA(4173, 1048639, F4, 18, 16) (dual of [(1048639, 18), 18875329, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4173, 4194557, F4, 2, 16) (dual of [(4194557, 2), 8388941, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4173, 4194558, F4, 2, 16) (dual of [(4194558, 2), 8388943, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(429, 257, F4, 2, 8) (dual of [(257, 2), 485, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (21, 29, 257)-net over F4, using
- base reduction for projective spaces (embedding PG(7,256) in PG(28,4)) for nets [i] based on digital (0, 8, 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(7,256) in PG(28,4)) for nets [i] based on digital (0, 8, 257)-net over F256, using
- extracting embedded OOA [i] based on digital (21, 29, 257)-net over F4, using
- linear OOA(4144, 4194301, F4, 2, 16) (dual of [(4194301, 2), 8388458, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4144, 8388602, F4, 16) (dual of [8388602, 8388458, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- OOA 2-folding [i] based on linear OA(4144, 8388602, F4, 16) (dual of [8388602, 8388458, 17]-code), using
- linear OOA(429, 257, F4, 2, 8) (dual of [(257, 2), 485, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(4173, 4194558, F4, 2, 16) (dual of [(4194558, 2), 8388943, 17]-NRT-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.