Information on Result #1202820
Digital (54, 74, 53180)-net over F81, using net defined by OOA based on linear OOA(8174, 53180, F81, 22, 20) (dual of [(53180, 22), 1169886, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8174, 265901, F81, 2, 20) (dual of [(265901, 2), 531728, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8174, 265904, F81, 2, 20) (dual of [(265904, 2), 531734, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8116, 182, F81, 2, 10) (dual of [(182, 2), 348, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(815, 82, F81, 2, 5) (dual of [(82, 2), 159, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;159,81) [i]
- linear OOA(8111, 100, F81, 2, 10) (dual of [(100, 2), 189, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,189P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OOA(815, 82, F81, 2, 5) (dual of [(82, 2), 159, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- 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(8116, 182, F81, 2, 10) (dual of [(182, 2), 348, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8174, 265904, F81, 2, 20) (dual of [(265904, 2), 531734, 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.