MinT - Information on Result #810699

Information on Result #810699

Linear OOA(2²²⁹, 172, F₂, 2, 65) (dual of [(172, 2), 115, 66]-NRT-code), using OOA 2-folding based on linear OA(2²²⁹, 344, F₂, 65) (dual of [344, 115, 66]-code), using

discarding factors / shortening the dual code based on linear OA(2²²⁹, 345, F₂, 65) (dual of [345, 116, 66]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16⁴⁰, 69, F₁₆, 32) (dual of [69, 29, 33]-code), using
    - constructionÂ X applied to AG(F,31P) âŠ‚ AG(F,34P) [i] based on
      1. linear OA(16³⁸, 64, F₁₆, 32) (dual of [64, 26, 33]-code), using algebraic-geometric code AG(F,31P) [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(16³⁵, 64, F₁₆, 29) (dual of [64, 29, 30]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16², 5, F₁₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
        discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [i]
  2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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.