Information on Result #1199246
Digital (44, 57, 174778)-net over F32, using net defined by OOA based on linear OOA(3257, 174778, F32, 14, 13) (dual of [(174778, 14), 2446835, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3257, 524335, F32, 2, 13) (dual of [(524335, 2), 1048613, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3257, 524337, F32, 2, 13) (dual of [(524337, 2), 1048617, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(327, 44, F32, 2, 6) (dual of [(44, 2), 81, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,81P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- linear OOA(3250, 524293, F32, 2, 13) (dual of [(524293, 2), 1048536, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3250, 1048586, F32, 13) (dual of [1048586, 1048536, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(3249, 1048577, F32, 13) (dual of [1048577, 1048528, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(3241, 1048577, F32, 11) (dual of [1048577, 1048536, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- OOA 2-folding [i] based on linear OA(3250, 1048586, F32, 13) (dual of [1048586, 1048536, 14]-code), using
- linear OOA(327, 44, F32, 2, 6) (dual of [(44, 2), 81, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3257, 524337, F32, 2, 13) (dual of [(524337, 2), 1048617, 14]-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.