Information on Result #1189514
Digital (112, 137, 1307)-net over F5, using net defined by OOA based on linear OOA(5137, 1307, F5, 27, 25) (dual of [(1307, 27), 35152, 26]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(5137, 5229, F5, 3, 25) (dual of [(5229, 3), 15550, 26]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(515, 16, F5, 3, 12) (dual of [(16, 3), 33, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,35P) [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- linear OOA(5122, 5213, F5, 3, 25) (dual of [(5213, 3), 15517, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5122, 15639, F5, 25) (dual of [15639, 15517, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(5109, 15626, F5, 23) (dual of [15626, 15517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- OOA 3-folding [i] based on linear OA(5122, 15639, F5, 25) (dual of [15639, 15517, 26]-code), using
- linear OOA(515, 16, F5, 3, 12) (dual of [(16, 3), 33, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
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.