Information on Result #1203894
Digital (55, 75, 209775)-net over F128, using net defined by OOA based on linear OOA(12875, 209775, F128, 22, 20) (dual of [(209775, 22), 4614975, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(12875, 1048876, F128, 2, 20) (dual of [(1048876, 2), 2097677, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12875, 1048877, F128, 2, 20) (dual of [(1048877, 2), 2097679, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12817, 300, F128, 2, 10) (dual of [(300, 2), 583, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1286, 150, F128, 2, 5) (dual of [(150, 2), 294, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,294P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12811, 150, F128, 2, 10) (dual of [(150, 2), 289, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,289P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150 (see above)
- linear OOA(1286, 150, F128, 2, 5) (dual of [(150, 2), 294, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12858, 1048577, F128, 2, 20) (dual of [(1048577, 2), 2097096, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12858, 2097154, F128, 20) (dual of [2097154, 2097096, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- OOA 2-folding [i] based on linear OA(12858, 2097154, F128, 20) (dual of [2097154, 2097096, 21]-code), using
- linear OOA(12817, 300, F128, 2, 10) (dual of [(300, 2), 583, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(12875, 1048877, F128, 2, 20) (dual of [(1048877, 2), 2097679, 21]-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.