MinT - Information on Result #1297302

Information on Result #1297302

Linear OA(2¹⁶⁶, 207, F₂, 58) (dual of [207, 41, 59]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2¹⁵⁹, 199, F₂, 58) (dual of [199, 40, 59]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶⁰, 200, F₂, 59) (dual of [200, 40, 60]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹⁵, 25, F₁₆, 14) (dual of [25, 10, 15]-code), using
      - extended algebraic-geometric code AG_e(F,10P) [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(2¹⁵⁹, 200, F₂, 51) (dual of [200, 41, 52]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2¹⁵⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 507373 505502 947105 220897 314665 624927 120735 310564 [i]
linear OA(2⁶, 7, F₂, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,2)), using
- dual of repetition code with length 7 [i]

Mode: Linear.

None.

None.