MinT - Information on Result #661690

Information on Result #661690

Linear OA(16¹¹⁸, 136, F₁₆, 86) (dual of [136, 18, 87]-code), using juxtaposition based on

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]
linear OA(16⁵³, 71, F₁₆, 44) (dual of [71, 18, 45]-code), using
- constructionÂ X applied to AG(F,19P) âŠ‚ AG(F,23P) [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(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(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
    - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
      - Reedâ€“Solomon code RS(13,16) [i]

Mode: Constructive and linear.

None.

The following results depend on this result: