MinT - Information on Result #858584

Information on Result #858584

Linear OOA(16⁹², 260, F₁₆, 2, 45) (dual of [(260, 2), 428, 46]-NRT-code), using OOA 2-folding based on linear OA(16⁹², 520, F₁₆, 45) (dual of [520, 428, 46]-code), using

trace code [i] based on linear OA(256⁴⁶, 260, F₂₅₆, 45) (dual of [260, 214, 46]-code), using
- constructionÂ X applied to AG(F, Q+104P) âŠ‚ AG(F, Q+105P) [i] based on
  1. linear OA(256⁴⁵, 257, F₂₅₆, 45) (dual of [257, 212, 46]-code or 257-arc in PG(44,256)), using algebraic-geometric code AG(F, Q+104P) 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]
  2. linear OA(256⁴³, 257, F₂₅₆, 43) (dual of [257, 214, 44]-code or 257-arc in PG(42,256)), using algebraic-geometric code AG(F, Q+105P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

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.