MinT - Information on Result #2217317

Information on Result #2217317

Linear OA(16¹¹⁶, 132, F₁₆, 87) (dual of [132, 16, 88]-code), using strength reduction based on linear OA(16¹¹⁶, 132, F₁₆, 88) (dual of [132, 16, 89]-code), using

juxtaposition [i] based on
1. linear OA(16⁴⁹, 65, F₁₆, 43) (dual of [65, 16, 44]-code), using
  - extended algebraic-geometric code AG_e(F,21P) [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(16⁵¹, 67, F₁₆, 44) (dual of [67, 16, 45]-code), using
  - constructionÂ X applied to AG(F,19P) âŠ‚ AG(F,21P) [i] based on
    1. linear OA(16⁵⁰, 64, F₁₆, 44) (dual of [64, 14, 45]-code), using algebraic-geometric code AG(F,19P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    2. linear OA(16⁴⁸, 64, F₁₆, 42) (dual of [64, 16, 43]-code), using algebraic-geometric code AG(F,21P) [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]

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.