Information on Result #1202816
Digital (52, 72, 53174)-net over F81, using net defined by OOA based on linear OOA(8172, 53174, F81, 22, 20) (dual of [(53174, 22), 1169756, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8172, 265871, F81, 2, 20) (dual of [(265871, 2), 531670, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8172, 265872, F81, 2, 20) (dual of [(265872, 2), 531672, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8114, 150, F81, 2, 10) (dual of [(150, 2), 286, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,289P) [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- linear OOA(8158, 265722, F81, 2, 20) (dual of [(265722, 2), 531386, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8158, 531444, F81, 20) (dual of [531444, 531386, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8155, 531441, F81, 19) (dual of [531441, 531386, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(8158, 531444, F81, 20) (dual of [531444, 531386, 21]-code), using
- linear OOA(8114, 150, F81, 2, 10) (dual of [(150, 2), 286, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8172, 265872, F81, 2, 20) (dual of [(265872, 2), 531672, 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.