MinT - Information on Result #856812

Information on Result #856812

Linear OOA(16⁵⁶, 279, F₁₆, 2, 21) (dual of [(279, 2), 502, 22]-NRT-code), using OOA 2-folding based on linear OA(16⁵⁶, 558, F₁₆, 21) (dual of [558, 502, 22]-code), using

discarding factors / shortening the dual code based on linear OA(16⁵⁶, 559, F₁₆, 21) (dual of [559, 503, 22]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16¹⁴, 45, F₁₆, 10) (dual of [45, 31, 11]-code), using
    - extended algebraic-geometric code AG_e(F,34P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]
  2. linear OA(16⁴², 514, F₁₆, 21) (dual of [514, 472, 22]-code), using
    - trace code [i] based on linear OA(256²¹, 257, F₂₅₆, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using
      - extended Reedâ€“Solomon code RS_e(236,256) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 257Â | 256²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      - algebraic-geometric code AG(F, Q+116P) 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+77P) 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,47P) 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.