MinT - Information on Result #857609

Information on Result #857609

Linear OOA(16⁸⁶, 293, F₁₆, 2, 31) (dual of [(293, 2), 500, 32]-NRT-code), using OOA 2-folding based on linear OA(16⁸⁶, 586, F₁₆, 31) (dual of [586, 500, 32]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸⁶, 587, F₁₆, 31) (dual of [587, 501, 32]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16²², 67, F₁₆, 15) (dual of [67, 45, 16]-code), using
    - constructionÂ X applied to AG(F,48P) âŠ‚ AG(F,50P) [i] based on
      1. linear OA(16²¹, 64, F₁₆, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [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(16¹⁹, 64, F₁₆, 13) (dual of [64, 45, 14]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(16⁶⁴, 520, F₁₆, 31) (dual of [520, 456, 32]-code), using
    - trace code [i] based on linear OA(256³², 260, F₂₅₆, 31) (dual of [260, 228, 32]-code), using
      - constructionÂ X applied to AG(F, Q+111P) âŠ‚ AG(F, Q+112P) [i] based on
        linear OA(256³¹, 257, F₂₅₆, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using algebraic-geometric code AG(F, Q+111P) 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]
        linear OA(256²⁹, 257, F₂₅₆, 29) (dual of [257, 228, 30]-code or 257-arc in PG(28,256)), using algebraic-geometric code AG(F, Q+112P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
        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.