MinT - Information on Result #2217425

Information on Result #2217425

Linear OA(16¹²², 140, F₁₆, 87) (dual of [140, 18, 88]-code), using strength reduction based on linear OA(16¹²², 140, F₁₆, 88) (dual of [140, 18, 89]-code), using

juxtaposition [i] based on
1. linear OA(16⁴⁷, 65, F₁₆, 41) (dual of [65, 18, 42]-code), using
  - extended algebraic-geometric code AG_e(F,23P) [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(16⁵⁷, 75, F₁₆, 46) (dual of [75, 18, 47]-code), using
  - constructionÂ X applied to AG(F,17P) âŠ‚ AG(F,23P) [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(16⁴⁶, 64, F₁₆, 40) (dual of [64, 18, 41]-code), using algebraic-geometric code AG(F,23P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16⁵, 11, F₁₆, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,16)), using
      - discarding factors / shortening the dual code based on linear OA(16⁵, 16, F₁₆, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
        Reedâ€“Solomon code RS(11,16) [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.