MinT - Information on Result #858594

Information on Result #858594

Linear OOA(16¹¹⁸, 289, F₁₆, 2, 45) (dual of [(289, 2), 460, 46]-NRT-code), using OOA 2-folding based on linear OA(16¹¹⁸, 578, F₁₆, 45) (dual of [578, 460, 46]-code), using

discarding factors / shortening the dual code based on linear OA(16¹¹⁸, 579, F₁₆, 45) (dual of [579, 461, 46]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16²⁸, 65, F₁₆, 22) (dual of [65, 37, 23]-code), using
    - extended algebraic-geometric code AG_e(F,42P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]
  2. linear OA(16⁹⁰, 514, F₁₆, 45) (dual of [514, 424, 46]-code), using
    - trace code [i] based on linear OA(256⁴⁵, 257, F₂₅₆, 45) (dual of [257, 212, 46]-code or 257-arc in PG(44,256)), using
      - extended Reedâ€“Solomon code RS_e(212,256) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 257Â | 256²âˆ’1, defining interval IÂ =Â [0,22], and minimum distance dÂ â‰¥ |{−22,−21,…,22}|+1Â =Â 46 (BCH-bound) [i]
      - algebraic-geometric code AG(F, Q+104P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
      - algebraic-geometric code AG(F, Q+69P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
      - algebraic-geometric code AG(F, Q+41P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.