Information on Result #1724240
Digital (113, 141, 3057)-net over F5, using net defined by OOA based on linear OOA(5141, 3057, F5, 33, 28) (dual of [(3057, 33), 100740, 29]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(5141, 15286, F5, 3, 28) (dual of [(15286, 3), 45717, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5141, 15290, F5, 3, 28) (dual of [(15290, 3), 45729, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5141, 15290, F5, 28) (dual of [15290, 15149, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(5141, 15657, F5, 28) (dual of [15657, 15516, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(58, 32, F5, 4) (dual of [32, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(58, 52, F5, 4) (dual of [52, 44, 5]-code), using
- trace code [i] based on linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
- extended Reed–Solomon code RSe(22,25) [i]
- algebraic-geometric code AG(F, Q+9P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F,7P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- trace code [i] based on linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(58, 52, F5, 4) (dual of [52, 44, 5]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(5141, 15657, F5, 28) (dual of [15657, 15516, 29]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5141, 15290, F5, 28) (dual of [15290, 15149, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(5141, 15290, F5, 3, 28) (dual of [(15290, 3), 45729, 29]-NRT-code), using
Mode: 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.