MinT - Information on Result #1297320

Information on Result #1297320

Linear OA(2¹⁷², 209, F₂, 62) (dual of [209, 37, 63]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2¹⁶³, 199, F₂, 62) (dual of [199, 36, 63]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶⁴, 200, F₂, 63) (dual of [200, 36, 64]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹⁶, 25, F₁₆, 15) (dual of [25, 9, 16]-code), using
      - extended algebraic-geometric code AG_e(F,9P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 25, using
        sharp bound on the number of rational points on curves with genus 1 [i]
    2. linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
      - Reedâ€“Muller code RM(1,3) [i]
      - caps in base bÂ =Â 2 [i]
linear OA(2¹⁶³, 200, F₂, 53) (dual of [200, 37, 54]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2¹⁶³Â > V_b^sâˆ’1(kâˆ’1)Â = 4 332311 192752 023072 361664 687507 783086 144366 555964 [i]
linear OA(2⁸, 9, F₂, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,2)), using
- dual of repetition code with length 9 [i]

Mode: Linear.

None.

None.