MinT - Information on Result #857993

Information on Result #857993

Linear OOA(16⁹⁶, 289, F₁₆, 2, 36) (dual of [(289, 2), 482, 37]-NRT-code), using OOA 2-folding based on linear OA(16⁹⁶, 578, F₁₆, 36) (dual of [578, 482, 37]-code), using

discarding factors / shortening the dual code based on linear OA(16⁹⁶, 579, F₁₆, 36) (dual of [579, 483, 37]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16²⁴, 65, F₁₆, 18) (dual of [65, 41, 19]-code), using
    - extended algebraic-geometric code AG_e(F,46P) [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(16⁷², 514, F₁₆, 36) (dual of [514, 442, 37]-code), using
    - trace code [i] based on linear OA(256³⁶, 257, F₂₅₆, 36) (dual of [257, 221, 37]-code or 257-arc in PG(35,256)), using
      - extended Reedâ€“Solomon code RS_e(221,256) [i]
      - algebraic-geometric code AG(F,110P) 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, Q+72P) 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,44P) with 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.