MinT - Information on Result #2254730

Information on Result #2254730

Linear OA(16¹¹⁷, 131, F₁₆, 91) (dual of [131, 14, 92]-code), using 1 times truncation based on linear OA(16¹¹⁸, 132, F₁₆, 92) (dual of [132, 14, 93]-code), using

juxtaposition [i] based on
1. linear OA(16⁵¹, 65, F₁₆, 45) (dual of [65, 14, 46]-code), using
  - extended algebraic-geometric code AG_e(F,19P) [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(16⁵³, 67, F₁₆, 46) (dual of [67, 14, 47]-code), using
  - constructionÂ X applied to AG(F,17P) âŠ‚ AG(F,19P) [i] based on
    1. linear OA(16⁵², 64, F₁₆, 46) (dual of [64, 12, 47]-code), using algebraic-geometric code AG(F,17P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    2. 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)
    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.