MinT - Information on Result #857841

Information on Result #857841

Linear OOA(16⁹¹, 289, F₁₆, 2, 34) (dual of [(289, 2), 487, 35]-NRT-code), using OOA 2-folding based on linear OA(16⁹¹, 578, F₁₆, 34) (dual of [578, 487, 35]-code), using

discarding factors / shortening the dual code based on linear OA(16⁹¹, 579, F₁₆, 34) (dual of [579, 488, 35]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16²³, 65, F₁₆, 17) (dual of [65, 42, 18]-code), using
    - extended algebraic-geometric code AG_e(F,47P) [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(16⁶⁸, 514, F₁₆, 34) (dual of [514, 446, 35]-code), using
    - trace code [i] based on linear OA(256³⁴, 257, F₂₅₆, 34) (dual of [257, 223, 35]-code or 257-arc in PG(33,256)), using
      - extended Reedâ€“Solomon code RS_e(223,256) [i]
      - algebraic-geometric code AG(F,111P) with 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,74P) with 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+44P) with degQ = 2 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.