MinT - Information on Result #856670

Information on Result #856670

Linear OOA(16⁴⁶, 266, F₁₆, 2, 19) (dual of [(266, 2), 486, 20]-NRT-code), using OOA 2-folding based on linear OA(16⁴⁶, 532, F₁₆, 19) (dual of [532, 486, 20]-code), using

trace code [i] based on linear OA(256²³, 266, F₂₅₆, 19) (dual of [266, 243, 20]-code), using
- constructionÂ X applied to AG(F, Q+47P) âŠ‚ AG(F, Q+48P) [i] based on
  1. linear OA(256¹⁹, 257, F₂₅₆, 19) (dual of [257, 238, 20]-code or 257-arc in PG(18,256)), using algebraic-geometric code AG(F, Q+117P) 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(256¹⁴, 257, F₂₅₆, 14) (dual of [257, 243, 15]-code or 257-arc in PG(13,256)), using algebraic-geometric code AG(F,121P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256⁴, 9, F₂₅₆, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,256)), using
    - discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
      - Reedâ€“Solomon code RS(252,256) [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.