Information on Result #1723264
Digital (125, 144, 453243)-net over F5, using net defined by OOA based on linear OOA(5144, 453243, F5, 21, 19) (dual of [(453243, 21), 9517959, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(5144, 1359730, F5, 3, 19) (dual of [(1359730, 3), 4079046, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 1359730, F5, 19) (dual of [1359730, 1359586, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 1953169, F5, 19) (dual of [1953169, 1953025, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(5136, 1953125, F5, 19) (dual of [1953125, 1952989, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(58, 44, F5, 4) (dual of [44, 36, 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(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(5144, 1953169, F5, 19) (dual of [1953169, 1953025, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 1359730, F5, 19) (dual of [1359730, 1359586, 20]-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.