MinT - Information on Result #856185

Information on Result #856185

Linear OOA(16²⁵, 265, F₁₆, 2, 10) (dual of [(265, 2), 505, 11]-NRT-code), using OOA 2-folding based on linear OA(16²⁵, 530, F₁₆, 10) (dual of [530, 505, 11]-code), using

discarding factors / shortening the dual code based on linear OA(16²⁵, 531, F₁₆, 10) (dual of [531, 506, 11]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16⁵, 17, F₁₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,16)), using
    - extended Reedâ€“Solomon code RS_e(12,16) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
  2. linear OA(16²⁰, 514, F₁₆, 10) (dual of [514, 494, 11]-code), using
    - trace code [i] based on linear OA(256¹⁰, 257, F₂₅₆, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using
      - extended Reedâ€“Solomon code RS_e(247,256) [i]
      - algebraic-geometric code AG(F,123P) 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,82P) 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+48P) 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.