MinT - Information on Result #857530

Information on Result #857530

Linear OOA(16⁸¹, 289, F₁₆, 2, 30) (dual of [(289, 2), 497, 31]-NRT-code), using OOA 2-folding based on linear OA(16⁸¹, 578, F₁₆, 30) (dual of [578, 497, 31]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸¹, 579, F₁₆, 30) (dual of [579, 498, 31]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16²¹, 65, F₁₆, 15) (dual of [65, 44, 16]-code), using
    - extended algebraic-geometric code AG_e(F,49P) [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(16⁶⁰, 514, F₁₆, 30) (dual of [514, 454, 31]-code), using
    - trace code [i] based on linear OA(256³⁰, 257, F₂₅₆, 30) (dual of [257, 227, 31]-code or 257-arc in PG(29,256)), using
      - extended Reedâ€“Solomon code RS_e(227,256) [i]
      - algebraic-geometric code AG(F,113P) 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+74P) 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+44P) 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.