Information on Result #1737518
Digital (56, 83, 2235)-net over F25, using net defined by OOA based on linear OOA(2583, 2235, F25, 30, 27) (dual of [(2235, 30), 66967, 28]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OOA(2583, 15646, F25, 2, 27) (dual of [(15646, 2), 31209, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2583, 15651, F25, 2, 27) (dual of [(15651, 2), 31219, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2583, 15651, F25, 27) (dual of [15651, 15568, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(18) [i] based on
- linear OA(2576, 15625, F25, 27) (dual of [15625, 15549, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- extended Reed–Solomon code RSe(19,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F,9P) with 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,6P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- construction X applied to Ce(26) ⊂ Ce(18) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2583, 15651, F25, 27) (dual of [15651, 15568, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2583, 15651, F25, 2, 27) (dual of [(15651, 2), 31219, 28]-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.